Jerzy Neyman, 1894 - 1981

By

Erich Lehmann

Technical Report No. 155May 1988

Research Supported by National Science Foundation Grant No. DMS84-01388

Department of StatisticsUniversity of CalifomiaBerkeley, California

Jerzy Neyman, 1894 - 1981*

Early years. Jerzy Neyman was born in Bendery (Russia) to parents of Polish ances-try. His full name with title - Splawa-Neyman - the first part of which he dropped atage 30, reflects membership in the polish nobility. Neyman's father Czeslaw, whodied when Jerzy was 12, was a lawyer and later judge, and an enthusiastic amateurarchaeologist. Since the family had been prohibited by the Russian authorities fromliving in Central Poland, then under Russian domination, Neyman grew up in Russia:in Kherson, Melitopol, and Simferopol, and (after his father's death) in Kharkov,where in 1912 he entered the University.

At Kharkov, Neyman was first interested in physics but because of his clumsinessin the Laboratory he abandoned it in favor of mathematics. On reading Lebesgue's"Lecons sur l'integration et la recherche des fonctions primitives", he later wrote (inFestschrift in honor of Herman Wold (1970)): "I became emotionally involved. Ispent the summer of 1915 at a country estate, coaching the son of the owner. Therewere three summer houses on the estate, filled with young people, including girlswhom I found beautiful and most attractive. However, the involvement with sets,measure and integration proved stronger than the charms of young ladies and most ofmy time was spent either in my room or on the adjacent balcony either on study or onmy first efforst at new results, intended to fill in a few gaps that I found in Lebesgue".A manuscript on Lebesgue integration (500 pages, handwritten) that he submitted to aprize competition won a gold medal.

One of his mentors at Kharkov was Serge Bernstein who lectured on probabilitytheory and statistics (including application of the latter to agriculture), subjects that didnot particularly interest Neyman. Nevertheless, he later acknowledged the influence ofBernstein from whom he "tried to acquire his tendency on concentrating on some 'bigproblem'." It was also Bernstein who introduced him to Karl Pearson's Grammar ofScience, which made a deep impression.

After the first World War, Poland regained its independence but soon becameembroiled in a war with Russia over borders. Neyman was jailed as an enemy alien;in 1921, in an exchange of prisoners, he finally went to Poland for the first time at theage of 27.

* A condensed version of this report is scheduled to appear in a Supplementto the Dictionary of Scientific Biography.

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In Warsaw, he established contact with Sierpinski, one of the founders of the jour-nal Fundamenta Mathematicae, which published one of Neyman's gold medal results(Vol.5 1923, 328-330). Although Neyman's heart was in pure mathematics, the statis-tics he had learned from Bernstein was more marketable and enabled him to obtain aposition as (the only) statistician at the Agricultural Institute in Bydgoszcz (formerlyBromberg). There, during 1921/22, he produced several papers on the application ofprobabilistic ideas to agricultural experimentation. In the light of Neyman's laterdevelopment, this work is of interest because of its introduction of probability modelsfor the phenomena being studied, particularly a randomization model for the case of acompletely randomized experiment. (For more details of Neyman's treatment seeScheff6, Ann. Math. Stat. 27 (1956) p.269.) He had learned the philosophy of such anapproach from Karl Pearson's book, where great stress is laid on models as mentalconstructs whose formulation constitutes the essence of science.*

In December 1922 Neyman gave up his job in Bydgoszcz to take charge of equip-ment and observations at the State Meteorological Institute, a change that enabled himto move to Warsaw. He did not like the work and soon left this position to become anAssistant at the University of Warsaw and Special Lecturer in mathematics and statis-tics at the Central College of Agriculture; he also gave regular lectures at the Univer-sity of Krakow. In 1924 he obtained his doctorate from the University of Warsawwith a thesis based on the papers he had written at Bydgoszcz.

Since no one in Poland was able to gauge the importance of his statistical work (hewas "suii generis", as he later described himself), the Polish authorities provided anopportunity for him to establish his credibility through publication in British journals.For this purpose they gave him a Fellowship to work with Karl Pearson in London.He did publish three papers in Biometrika (based in part on his earlier work), butscientifically the academic year (1925/26) spent in Pearson's Laboratory was a disap-pointment. Neyman found the work of the Laboratory old-fashioned and Pearson him-self surprisingly ignorant of modern mathematics. (The fact that Pearson did notunderstand the difference between independence and lack of correlation led to amisunderstanding that nearly terminated Neyman's stay at the Laboratory.) So when,with the help of Pearson and Sierpinski, he received a Rockfeller Fellowship that madeit possible for him to stay in the West for another year, he decided to spend it in Parisrather than in London.

*"'One of my favorite ideas", Neyman later wrote in 1957 (Rev. Int. Stat. Inst.25, p.8), "learned from Mach via Karl Pearson's 'Grammar of Science', is thatscientific theories are no more than models of natural phenomena".

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There he attended the lectures of Lebesgue and a seminar of Hadamard, "I felt thatthis was real mathematics worth studying" he wrote later, "and, were it not for EgonPearson, I would have probably drifted to my earlier passion for sets, measure andintegration, and returned to Poland as a faithful member of the Warsaw school and asteady contributor to Fundamenta Mathematicae."

The Neyman Pearson Theory. What pulled Neyman back into statistics was a letterhe received in the Fall of 1926 from Egon Pearson, Karl Pearson's son, with whomNeyman had had only little contact in London. Egon had begun to question therationale underlying some of the current work in statistics, and the letter outlined hisconcerns. Correspondence developed and, reinforced by occasional joint holidays,continued when at the end of the Rockefeller year Neyman returned to a hectic anddifficult life in Warsaw. He continued to lecture at the University (as Docent after hishabilitation in 1928), at the Central College of Agriculture, and at the University ofKrakow. In addition, he founded a small statistical Laboratory at the Nencki Institutefor Experimental Biology. To supplement his meager academic income, and to pro-vide financial support for the young students and coworkers in his Laboratory, he tookon a variety of consulting jobs. These involved different areas of application, with themajority coming from agriculture and from the Institute for Social Problems, the latterwork being concerned with Polish census data.

Neyman felt harassed, and his financial situation was always precarious. Thebright spot in this difficult period was his work with the younger Pearson. Trying tofind a unifying, logical basis which would lead systematically to the various statisticaltests that had been proposed by Student and Fisher was a "big problem" of the kindfor which he had hoped since his student days with Bernstein.

In 1933 Karl Pearson retired from his chair at University College, London, and hisposition was divided between R.A. Fisher and Neyman's friend and collaborator EgonPearson. The latter lost no time, and as soon as it became available, in the Spring of1934 offered Neyman a temporary position in his Laboratory. Neyman was enthusias-tic. This would greatly facilitate their joint work and bring relief to his Warsawdifficulties.

The set of issues addressed in the joint work of Neyman and Pearson between1926 and 1933 turned out indeed to be a "big problem," and their treatment of it esta-blished a new paradigm that changed the statistical landscape. What had concernedPearson when he first approached Neyman in 1926 was the ad hoc nature of the smallsample tests being studied by Fisher and Student. In his search for a general principlefrom which such tests could be derived, he had written to Student. Student in hisreply had suggested that one would be inclined to reject a hypothesis under which the

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observed sample is very improbable" if there is an alternative hypothesis which willexplain the occurrence of the sample with a more reasonable probability." (E.S. Pear-son in "Research Papers in Statistics", F.N. David, Ed. 1966). This comment ledPearson to propose to Neyman the likelihood ratio criterion, in which the maximumlikelihood of the observed sample under the alternatives under consideration is com-pared to its value under the hypothesis. During the next year Neyman and Pearsonstudied this and other approaches, and worked out likehood ratio tests for some impor-tant examples. They published their results in 1928 in a fundamental two-part paper,"On the use and interpretation of certain test criteria for purposes of statistical infer-ence". The paper contained many of the basic concepts of what was to become theNeyman-Pearson Theory of Hypothesis Testing; such as the two types of error, theidea of power, and the distinction between simple and composite hypotheses.

Although Pearson felt that the likelihood ratio provided the unified approach forwhich he had been looking, Neyman was not yet satisfied. It seemed to him that thelikelihood principle itself was somewhat ad hoc and had no fully logical basis. How-ever, in February 1930, he was able to write Pearson that he had found "a rigorousargument in favour of the likelihood method". His new approach consisted of maxim-izing the power of the test, subject to the condition that under the hypothesis (assumedto be simple) the rejection probability has a preassigned value (the level of the test).He reassured Pearson that in all cases he had examined so far this logically convincingtest coincided with the likelihood ratio test. A month later, Neyman announced toPearson that he now had a general solution of the problem of testing a simplehypothesis against a simple alternative. The result in question is of course the "Fun-damental Lemma", which plays such a crucial role in Neyman-Pearson theory.

The next step was to realize that in the case of more than one alternative theremight exist a uniformly most powerful test that would simultaneously maximize thepower for all of them. If such a test exists, Neyman found, it coincides with the likeli-hood ratio test but in the contrary case - alas - the likelihood ratio test may be biased.These results, together with many examples and elaborations, were published in 1933under the title, "On the Problem of the Most Efficient Tests of StatisticalHypotheses". While in the 1928 paper the initiative and insights had been those ofPearson who had had to explain to Neyman what he was doing, the situation was nowreversed with Neyman as leader and Pearson a somewhat reluctant follower.

The 1933 paper is the fundamental paper in the theory of hypothesis testing. Itestablished a framework for this theory* and states the problem of finding the best test

* Its role in today's statistical climate is discussed in Lehmann, "TheNeyman-Pearson theory after 50 years" (Proc. of the Berkeley Conference inhonor of Jerzy Neyman and Jack Kiefer, Vol 1, 1-14. Wadsworth, 1985.

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as a clearly formulated, logically convincing mathematical problem that one can thenproceed to solve. Its importance transcends the theory of hypothesis testing since itprovided also the inspiration for Wald's later, much more general statistical decisiontheory.

Survey sampling and confidence estimation. In the following year Neyman pub-lished another landmark paper. An elaboration of work on survey sampling he haddone earlier for the Warsaw Institute for Social Problems, it was directed towardbringing clarity into a somewhat muddled discussion about the relative merits of twodifferent sampling methods. His treatment, described by Fisher as "luminous", intro-duced many important concepts and results and may be said to have initiated themodern theory of survey sampling.

The year 1935 brought two noteworthy events. The first was Neyman's appoint-ment to a permanent position of Reader (Assocciate Professor) in Pearson's Depart-ment. Although at the time he was still hoping eventually to return to Poland, he infact never did except for brief visits. The second event was the presentation at a meet-ing of the Royal Statistical Society of an important paper on agricultural experimenta-tion in which he raised some questions concerning Fisher's Latin Square design. Thiscaused a break in their hitherto friendly relationship and was the beginning of lifelongdisputes. (Fisher, who opened the discussion of the paper, stated that "he had hopedthat Dr. Neyman's paper would be on a subject with which the author was fullyacquainted, and on which he could speak with authority, as in the case of his addressto the Society last summer. Since seeing the paper, he had come to the conclusionthat Dr. Neyman had been somewhat unwise in his choice of topics".)

Neyman was to remain in England for four years (1934-38). During this time hecontinued his collaboration with Egon Pearson on the theory and applications ofoptimal tests, efforts that also included contributions from graduate and postdoctoralstudents. To facilitate publication and to emphasize the unified point of view underly-ing this work, Neyman and Pearson set up a series, "Statistical Research Memoirs",published by University College and restricted to work done in the Department ofStatistics. A first volume appeared in 1936, a second in 1938.

Another central problem occupying Neyman during his London years was thetheory of estimation: not point estimation in which a parameter is estimated by aunique number, but estimation by means of an interval or more general set in whichthe unknown parameter can be said to lie with specified confidence (i.e. probability).Such confidence sets are easily obtained under the Bayesian assumption that theparameter is itself random with known probability distribution, but Neyman's aim wasto dispense with such an assumption which he considered arbitrary and unwarranted.

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Neyman published brief accounts of his solution to this problem in 1934 and 1935and the theory in full generality in 1937 in "Outline of a Theory of Statistical Estima-tion Based on the Classical Theory of Probability" (Phil. Trans. Roy. Soc. Ser. AVol.236, 333-380). He had first submitted this paper to Biometrika, then being editedby Egon Pearson, but to his great disappointment, Pearson had rejected it as too longand too mathematical.

Neyman's approach was based on the idea of obtaining confidence sets S (X) for aparameter 0 from acceptance regions for the hypotheses that 0 = 00 by taking for S (X)the set of all parameter values 00 that would be accepted at the given level. This for-mulation established an equivalence between confidence sets and families of tests, andenabled him to transfer the test theory of the 1933 paper lock, stock, and barrel to thetheory of estimation. (Unbeknownst to Neyman, the idea of obtaining confidence setsby inverting an acceptance rule had already been used in special cases by Laplace [in alarge-sample binomial setting] and by Hotelling).

In his paper on survey sampling, Neyman had referred to the relationship of hisconfidence intervals to Fisher's fiducial limits, which appeared to give the same resultsalthough derived from a somewhat different point of view. In the discussion of thepaper, Fisher welcomed Neyman as an ally in the effort to free statistics from unwar-ranted Bayesian assumptions. He went on to say that "Dr. Neyman claimed to havegeneralized the argument of fiducial probability, and he had every reason to be proudof the line of argument he had developed for its perfect clarity. The generalizationwas a wide and very handsome one, but it had been erected at considerableexpense,...". He then proceeded to indicate the disadvantages he saw in Neyman'sformulation, of which perhaps the most important one (revealing the wide differencebetween their interpretations) was non-uniqueness. The debate between the two menover their respective approaches continued for many years, usually in less friendlyterms; it is reviewed by Neyman in "Silver jubilee of my dispute with Fisher (J.Operat. Res. Soc. of Japan (1961) 145-154).

Statistical Philosophy. During the period of his work with Pearson, Neyman's atti-tude toward probability and hypothesis testing gradually underwent a radical change.In 1926, he tended to favor a Bayesian approach* in the belief that any theory wouldhave to involve statements about the probabilities of various alternative hypotheses andhence an assumption of prior probabilities. In the face of Pearson's (and perhpas also

* In Frequentist Probability and Frequentist Statistics (Synthese 36 (1977)97-131, Neyman states, "I began as a quasi-Bayesian. My assumption was thatthe estimated parameter (just one!) is a particular value of a random variablehaving an unknown prior distribution."

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Fisher's) strongly anti-Bayesian position he became less certain, and in his papers ofthe late twenties (both alone and jointly with Pearson) he presented Bayesian and non-Bayesian approaches side by side. A decisive influence was von Mises' book"Wahrscheinlichkeit, Statistik und Wahrheit", (1928) about which he later wrote (inhis Author's Note to A Selection of Early Statistical Papers of J. Neyman) that it"confirmed him as a radical 'frequentist' intent on probability as a mathematical ideal-ization of relative frequency". He opposed any subjective approach to science, andremained an avowed frequentist for the rest of his life.

A second basic aspect of Neyman's work from the thirties on is a point of view,which he formulated clearly in the closing pages of his presentation at the 1937Geneva Conference: "L'estimation statistique trait6e comme un probl'me classique deprobabilit6" (Actual. Sci. et Industr. No 739, 25-57). His approach is not based oninductive reasoning, he states, but instead on the concept of "comportement inductif"or inductive behavior. That is, statistics is to be used not to extract from experience"beliefs" but as a guide to appropriate action.

He summarized his views in a paragraph in a paper presented in 1949 to the Inter-national Congress on the Philosophy of Science. (Foundations of the General Theoryof Estimation", Actual. Scie. et Industr. 1146 (1951) p. 85).

"Why abandon the phrase 'inductive reasoning' in favor of 'inductive behavior'? Asexplained in 1937*, the term inductive reasoning does not seem appropriate to describethe new method of estimation because all the reasoning behind this method is clearlydeductive. Starting with whatever is known about the distribution of the observablevariables X, we deduce the general form of the functions f(X) and g (X) which havethe properties of confidence limits. Once a class of such pairs of functions is found,we formulate some properties of these functions which may be considered desirableand deduce either the existence or non-existence of an "optimum" pair, etc. Once thevarious possibilities are investigated we may decide to use a particular pair ofconfidence limits for purposes of statistical estimation. This decision, however, is not'reasoning'. This is an act of will just as the decision to buy insurance is an act ofwill. Thus, the mental processes behind the new method of estimation consist ofdeductive reasoning and of an act of will. In these circumstances the term 'inductivereasoning' is out of place and, if one wants to keep the adjective 'inductive', it seemsmost appropriate to attach to it the noun 'behavior'.

* loc. cit.

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In other writings (for example in Rev. Internat. Statist. Inst. 25 (1957) 7-22), Ney-man acknowledges that a very similar point of view was advocated by Gauss andLaplace. It is of course also that of Wald's later general statistical decision theory.On the other hand, this view was strongly attacked by Fisher (for example in JRSS (B)17 (1955) 69-78)) who maintained that decision making has no role in scientific infer-ence, and that his fiducial argument provides exactly the mechanism required for thispurpose.

Moving to America. By 1937, Neyman's work was becoming known not only inEngland and Poland but also in other parts of Europe and in America. He gave aninvited talk about the theory of estimation at the International Congress of Probabilityheld in 1937 in Geneva, and in the Spring of 1937 he spent six weeks in the UnitedStates on a lecture tour organized by S.S. Wilks. The visit included a week at theGraduate School of the Department of Agriculture in Washington arranged by EdwardDeming. There he gave three lectures and six conferences on the relevance of proba-bility theory to statistics, and on his work in hypothesis testing, estimation, sampling,and agricultural experimentation as illustrations of this approach. These "Lectures andConferences on Mathematical Statistics", which provided a coherent statement of thenew paradigm he had developed and exhibited its successful application to a numberof substantive problems, were a tremendous success. A mimeographed versionappeared in 1938 and was soon sold out. Neyman published an augmented secondedition in 1952.

After his return from the United States, Neyman debated whether to remain inEngland where he had a permanent position but little prospect of promotion andindependence, or to return to Poland. Then completely unexpectedly, in the Fall of1937 he received a letter from an unknown, G.C. Evans, chairman of the MathematicsDepartment at Berkeley, offering him a position in his department. Neyman hesitatedfor some time. California and its University were completely unknown quantities,while the situation in England - although not ideal - was reasonably satisfactory andstable. An attractive aspect of the Berkeley offer was the nonexistence there of anysystematic program in statistics, so that he would be free to follow his own ideas.What finally tipped the balance in favor of Berkeley was the threat of war in Europe.Thus in April 1938 he decided to accept the Berkeley offer and emigrate to America,with his wife Olga (from whom he later separated) and his 2-year old son Michael.He had just turned 44, and he would remain in Berkeley for the rest of his long life.

The Berkeley Department of Statistics. Neyman's top priority after his arrival inBerkeley was the development of a statistics program, that is, a systematic set of

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courses and a faculty to teach therm He quickly organized a number of core coursesand began to train some graduate students and one temporary instructor in his ownapproach to statistics. Administratively, he set up a Statistical Laboratory as a semi-autonomous unit within the Mathematics Department. However, soon America's entryinto World War II in 1941 put all further academic development on hold. Neymantook on war work, and for the next years this became the Laboratory's central and all-consuming activity. The work dealt with quite specific military problems and did notproduce results of lasting interest.

The building of a faculty began in earnest after the war, and by 1956 Neyman hadestablished a permanent staff of twelve members, many his own students, but alsoincluding three senior appointments from outside (Lobve, Scheff6, and Blackwell).Development of a substantial faculty, with the attendant problems of space, clericalstaff, summer support, and so on, represented a major, sustained administrative effort.A crucial issue in the growth of the program concerned the course offerings in basicstatistics by other departments. Although these involved major vested interests, Ney-man gradually concentrated the teaching of statistics within his statistics program, atleast at the lower division level. This was an important achievement both in establish-ing the identity of his program and in obtaining the student base which alone couldjustify the ongoing expansion of the Faculty. In his negotiations with the Administra-tion, Neyman was strengthened by the growing international reputation of his Labora-tory, and by the increasing post-war importance of the field of statistics itself.

An important factor in the Laboratory's reputation was the series of international"Symposia on Mathematical Statistics and Probability" that Neyman organized at 5-year intervals during 1945-1970, and the publication of their proceedings. The firstSyposium was held in August 1945 to celebrate the end of the war and "the return totheoretical research" after years of war work. The meeting, although rather modestcompared to the later symposia, was such a success that Neyman soon began to plananother one for 1950. In future years the Symposia grew in size, scope, and impor-tance and did much to establish Berkeley as a major statistical center.

The spectacular growth Neyman achieved for his group required a constant strugglewith various administrative authorities including those of the Mathematics Department.To decrease the number of obstacles, and also to provide greater visibility for thestatistics program, Neyman soon after his arrival in Berkeley began a long effort toobtain independent status for his group as a Department of Statistics. A separateDepartment finally became a reality in 1955, with Neyman as its chair. He resignedthe chairmanship the following year (but retained the Directorship of the Laboratory tothe end of his life). He felt, he wrote in his letter of resignation, that "the transforma-tion of the old Statistical Laboratory into a Department of Statistics closed a period of

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development ... and opened a new phase." In these circumstances, he stated "it is onlynatural to have a new and younger man take over."

There was perhaps another reason. Much of Neyman's energy during the nearlytwenty years he had been in Berkeley had gone into administration. His efforts hadbeen enormously successful: A first rate Departrnent, the Symposia, a large number ofgrants providing summer support for Faculty and students. It was a great accomplish-ment and his personal creation, but now it was time to get back more fully intoresearch.

Applied Statistics. Neyman's theoretical research in Berkeley was largely motivatedby his consulting work, one of the purposes for which the University had appointedhim and through which he made himself useful to the campus at large. Problems inAstronomy, for example led to the interesting insight (1948, joint with Scott) that max-imum likelihood estimates may cease to be consistent if the number of nuisanceparameters tends to infinity with increasing sample size. Also, to simplify maximumlikelihood computations, which in applications frequently became very cumbersome, hedeveloped linearized, asymptotically equivalent methods - his BAN (best asymptoti-cally normal) estimates (1949) - which have proved enormously. useful.

His major research efforts in Berkeley were devoted to several large-scale appliedprojects. These included questions regarding competition of species (with T. Park),accident proneness (with G. Bates), the distribution of galaxies and the expansion ofthe Universe (with C.D. Shane and particularly Elizabeth Scott who became a steadycollaborator and close companion), the effectiveness of cloud seeding, and a model forcarcinogenesis. Of these perhaps the most important was the work in astronomywhere the introduction of the Neyman-Scott clustering model brought new methodsinto the field which "were remarkable and perhaps have not yet been fully appreciatedand exploited." (Peeble: Large Scale Structure of the Universe; Princeton Univ. Press,1979).

Neyman's applicational work, although it extends over many different areas, exhi-bits certain common features, which he made explicit in some of his writings andwhich combine into a philosophy for applied statistics. The following are some of theprincipal aspects.

(1) The studies are indeterministic. Neyman has pointed out that the distinctionbetween deterministic and indeterministic studies lies not so much in the nature of thephenomena as in the treatment accorded to them. ("Indeterminism in Science andnew Demands on Statisticians". J. Amer. Statist. Assoc. 55 (1960) 625-639). In fact,many subjects that traditionally were treated as deterministic are now being viewedstochastically. Neyman himself has contributed to this change in several areas.

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(2) An indeterministic study of a scientific phenomenon involves the constructionof a stochastic model. In this connection, Neyman introduced the important distinctionbetween models that are interpolatory devices and those that embody genuine explana-tory theories. The latter he describes as "a set of reasonable assumptions regardingthe mechanism of the phenomena studied", while the former "by contrast consist ofthe selection of a relatively ad hoc family of functions, not deduced from underlyingassumptions, and indexed by a set of parameters." (Stochastic Models and their Appli-cation to Social Phenomena", joint with W. Kruskal; presented at a joint session ofIMS, ASA, and the Amer. Sociol. Soc., Sept. 1956.) The distinction is discussed ear-lier, and again later, in Neyman's papers in Ann. Math. Statist. 10 (1939) p.372/3 andin Reliability and Biometry. Siam. Philadelphia 1974, pp.185-188.

Neyman's favorite examples of the distinction between the two types were the fam-ily of Pearson curves, which for a time was very popular as an interpolatory modelthat could be fitted to many different data sets, and Mendel's model for heredity. "Atthe time of its invention", he wrote about the latter in J. Amer. Statist. Assoc.55(1960) 625-639) "this was little more than an interpolatory procedure invented tosummarize Mendel's experiments with peas", but eventually it turned out to satisfyNeyman's two criteria for a model of genuine scientific value, namely (i) broad appli-cability (i.e. in Mendel's case not restricted to peas), and (ii) identifiability of details(the genes as entities with identifiable location on the chromosomes).

Most actual modeling, Neyman points out, is intermediate between these twoextremes, often exhibiting features of both kdnds. Related is the realization that inves-tigators will tend to use as building blocks models which "partly through experienceand partly through imagination, appear to us familiar and, therefore, simple." ("Sto-chastic Models of Population Dynamics", Science 130 (1959) 303-308, joint withScott).

(3) To develop a 'genuine explanatory Theory' requires substantial knowledge ofthe scientific background of the problem. When the investigation concerns a branch ofscience with which the statistician is unfamiliar, this may require a considerableamount of work. For his collaboration with Scott in astronomy, Neyman studied theastrophysical literature, joined the American Astronomical Society, and became amember of the Commission on Galaxies of the International Astronomical Union.When he developed an interest in carcinogenesis, he spent three months at the NationalInstitutes of Health to leam more about the biological background of the problem.

Neyman summarizes his own attitude toward this kind of research in the closingsentence of his paper "A glance of my personal experiences in the process ofresearch" (in Scientists at work (1970); Almquist and Wicksell): "The elements thatare common ... seem to be my susceptibility to becoming emotionally involved in

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other individuals' interests and enthusiasm, whether these individuals are sympatheticor not, and, particularly in the more recent decades, the delight I experience in tryingto fathom the chance mechanisms of phenomena in the empirical world."

An avenue for learning about the state of the art in a field and bringing togetherdiverse points of view, which Neyman enjoyed and of which he made repeated use,was to arrange a conference. Two of these (on weather modification in 1965 and onmolecular Biology in 1970) became parts of the then current Symposia. In addition, in1961 jointly with Scott he arranged a "Conference on the Instability of Systems ofGalaxies," and finally in July 1981, jointly with Le Cam and on very short notice, anInterdisciplinary Cancer Conference.

Epilogue. A month after the cancer conference, Neyman died of heart failure at age87 on Aug. 5, 1981. He had been in reasonable health up to two weeks earlier, and onthe day before his death was still working in the hospital on a book on weathermodification.

Neyman is recognized as one of the founders of the modern theory of statistics,whose work on hypothesis testing, confidence intervals, and survey sampling has revo-lutionized both theory and practice. His enormous influence on the development ofstatistics is further greatly enhanced through the large number of his Ph. D. students.These are:

From Poland:Kolodziejczyk, Iwaszkiewicz, Wilenski, Ptykowski

From London:Hsu, David, Johnson, Eisenhart, Sukhatme, Beall, Sato, Shanawany, Jack-son, Tang

From Berkeley:Chen, Dantzig, Lehmann, Massey, Fix, Chapman, Eudey, Gurland,Hodges, Seiden, Hughes, Taylor, Jeeves, Le Cam, Tate, Chiang, Agarwal,Sane, Read, Singh, Borgman, Marcus, Buehler, Kulkarni, Davies,Clifford, Samuels, Oyelese, Ray, Grieg, Green, Tsiatis, Singh, Javitz,Darden.

His achievements were recognized by honorary degrees from the Universities ofChicago, California, Stockholm, and Warsaw, and from the Indian Statistical Institute.He was elected to the U.S. Academy of Sciences and to Foreign Membership in the

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Royal Society, the Royal Swedish Academy, and the Polish National Academy. Inaddition, he received many awards, including the U.S. National Medal of Science andthe Guy Medal in Gold of the U.K. Royal Statistical Society.

Neyman was completely and enthusiastically dedicated to his work, which filled hislife - there was not time for hobbies. Work, however, included not only research andteaching, but also their social aspects such as traveling to meetings and organizingconferences. Pleasing his guests was an avocation; his hospitality had an internationalreputation. In his Laboratory he created a family atmosphere that included students,colleagues, and visitors, with himself as pater familias.

As administrator, Neyman was indomitable. He would not take no for an answer,and was quite capable of resorting to unilateral actions. He firmly believed in therighteousness of his causes and found it difficult to understand how a reasonable per-son could disagree with him. At the same time, he had great charm that often washard to resist.

The characteristic that perhaps remains in mind above all is his generosity: further-ing the careers of his students, giving credit and doing more than his share in colla-boration, and extending his help (including financial assistance out of his own pocket)to anyone who needed it.

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Bibliography.

I. Original works.

A complete bibliography of Neyman's work is given at the end of David Kendall'sMemoir (Biographical Memoirs of Fellows of the Royal Society, Vol. 28, 1982).Some of the early papers are reprinted in the two volumes, "A Selection of Early Sta-tistical papers of J. Neyman" and "Joint Statistical Papers of J. Neyman and E.S.Pearson" (University of California Press). Neyman's letters to E.S. Pearson from1926-1933 (but not Pearson's replies) are preserved in Pearson's estate.

An overall impression of Neyman's ideas and style can be gained from his book,"Lectures and Conferences on Mathematical Statistics and Probability", Secondrevised and enlarged edition (Graduate School U.S. Department of Agriculture, 1952).The following partial list provides a more detailed view of his major theoretical contri-butions:

A. Paradigmatic Papers

"On the Use and Interpretation of Certain Test Criteria for Purposes of StatisticalInference", Biometrika 20A (1928), 175-240; 263-294 (with E.S. Pearson).

On the problem of the most efficient tests of statistical hypotheses. Phil. Trans.Roy. Soc. Lond. A 231, 1933, 289-337 (with E.S. Pearson).

On the two different aspects of the representative method. J. Roy. Statist. Soc. 97,1934, 558-625. (Spanish version of this paper appeared in Estadistica. J. Inter-Amer. Stat. Inst. 17, (1959) 587-651.)

Outline of a theory of statistical estimation based on the classical theory of proba-bility. Phil. Trans. Roy. Soc. Lond. A 203, 1937, 1211-1213.

B. Some other theoretical contributions.

'Smooth' test for goodness of fit. Skand. aktuar. Tidsskr. 20, 1937, 149-199.

On a new class of 'contagious' distributions, applicable in entomology and bac-teriology. Ann. Math. Statist. 10, 1939, 35-57.

Consistent estimates based on partially consistent observations. Econometrica 16,1948, 1-32 (with E.L. Scott).

Contribution to the theory of the chi-square test. Proc. Berkeley Symp. Math. Sta-tist. Probab. (ed. J. Neyman), pp.239-273. Berkeley: University of CaliforniaPress. 1949.

Optimal asymptotic tests of composite statistical hypotheses. Probability andstatistics (The Harald Cramer Volume), (ed. U. Granander), pp.213-234. Uppsala,

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Sweden: Almquist & Wiksells.Outlier proneness of phenomena and of related distributions. Optimizing methodsin statistics (ed. J.S. Rustagi), pp.413-430. New York and London: AcademicPress Inc. 1971 (with E.L. Scott).

Neyman's position regarding the role of statistics in science can be obtained fromthe following more philosophical and sometimes autobiographical articles.

Foundation of the general theory of statistical estimation. Actual Scient. Ind. No.1146, 83-95. 1951.

The problem of inductive inference. Commun Pure Appl. Math. VII, 1955, 13-45.'Inductive behavior' as a basic concept of philosophy of science. Revue Inst. Int.Statist. 2S, 1957, 7-22.

Stochastic models of population dynamics. Science N.Y. 130, 1959, 303-308 (withE.L. Scott).A glance at some of my personal experiences in the process of research. Scientistsat Work (ed. T. Dalenius. G. Karlsson & S. Malmquist), pp. 148-164. Uppsala,Sweden: Almquist & Wiksells. 1970.

Frequentist probability and frequentist statistics. Synthiese 36, 1977, 97-131.

II. Secondary Literature.The most important source for Neyman's life and personality is Constance Reid,

"Neyman - from Life" (Springer, 1982), which is based on Neyman's own recollec-tions (obtained during weekly meetings over a period of more than a year), those ofhis colleagues and former students, and on many original documents. A usefulaccount of his collaboration with E.S. Pearson was written by Pearson for the NeymanFestschrift, "Research Papers in Statistics" (F.N. David, Ed., Wiley, 1966). Addi-tional accounts of his life and work are provided by the following papers:

L. Le Cam and E.L. Lehmann, "J. Neyman - on the occasion of his 80-th birth-day". Ann. Statist. 2 (1974) vii-xiii.D.G. Kendall, M.S. Bartlett, and T.L. Page, "Jerzy Neman, 1894-1981" in Bio-graphical Memoirs of Fellows of the Royal Society 28 (1982) 379-412.E.L. Lehmann and Constance Reid, "In Memoriam - Jerzy Neyman, 1894-1981".The Amer. Statistician 36, (1982) 161/2.E.L. Scott, "Neyman, Jerzy" in Encycl. Statist. Sci. 6 (1985) 214-223.

TECHNICAL REPORTSStatistics Department

University of California, Berkeley

1. BREIMAN, L. and FREEDMAN, D. (Nov. 1981, revised Feb. 1982). How many variables should be entered in aregression equation? Jour. Amer. Statist. Assoc., March 1983, 78, No. 381, 131-136.

2. BRILLINGER, D. R. (Jan. 1982). Some contrasting examples of the time and frequency domain approaches to time seriesanalysis. Time Series Methods in Hydrosciences, (A. H. El-Shaarawi and S. R. Esterby, eds.) Elsevier ScientificPublishing Co., Amsterdam, 1982, pp. 1-15.

3. DOKSUM, K. A. (Jan. 1982). On the performance of estimates in proportional hazard and log-linear models. SurvivalAnalysis, (John Crowley and Richard A. Johnson, eds.) IMS Lecture Notes - Monograph Series, (Shanti S. Gupta. seriesed.) 1982, 74-84.

4. BICKEL, P. J. and BREIMAN, L. (Feb. 1982). Sums of functions of nearest neighbor distances, moment bounds, limittheorems and a goodness of fit test. Ann. Prob., Feb. 1982, 11. No. 1, 185-214.

5. BRILLINGER, D. R. and TUKEY, J. W. (March 1982). Spectrum estimation and system identification relying on aFourier transform. The Collected Works of J. W. Tukey, vol. 2, Wadsworth, 1985, 1001-1141.

6. BERAN, R. (May 1982). Jacklnife approximation to bootstrap estimates. Amn. Statist., March 1984, 12 No. 1, 101-118.

7. BICKEL, P. J. and FREEDMAN, D. A. (June 1982). Bootstrapping regression models with many parameters.Lehmann Festschrift, (P. J. Bickel, K. Doksum and J. L. Hodges, Jr., eds.) Wadsworth Press, Belmont, 1983, 2848.

8. BICKEL, P. J. and COLLINS, J. (March 1982). Minimizing Fisher information over mixtures of distributions. Sanhyl,1983, 45, Series A, Pt. 1, 1-19.

9. BREIMAN, L. and FRIEDMAN, J. (July 1982). Estimating optimal transformations for multiple regression and correlation.

10. FREEDMAN, D. A. and PETERS, S. (July 1982, revised Aug. 1983). Bootstrapping a regression equation: someempirical results. JASA, 1984, 79, 97-106.

11. EATON, M. L. and FREEDMAN, D. A. (Sept. 1982). A remark on adjusting for covariates in multiple regression.

12. BICKEL, P. J. (April 1982). Minimax estimation of the mean of a mean of a normal distribution subject to doing wellat a point. Recent Advances in Statistics, Academic Press, 1983.

14. FREEDMAN, D. A., ROTHENBERG, T. and SUTCH, R. (Oct. 1982). A review of a residential energy end use model.

15. BRILLINGER, D. and PREISLER, H. (Nov. 1982). Maximum likelihood estimation in a latent variable problem. Studiesin Econometrics, Time Series, and Multivariate Statistics, (eds. S. Karlin, T. Amemiya, L. A. Goodman). AcademicPress, New York, 1983, pp. 31-65.

16. BICKEL, P. J. (Nov. 1982). Robust regression based on infinitesimal neighborhoods. Ann. Statist., Dec. 1984, 12,1349-1368.

17. DRAPER, D. C. (Feb. 1983). Rank-based robust analysis of linear models. I. Exposition and review.

18. DRAPER, D. C. (Feb 1983). Rank-based robust inference in regression models with several observations per cell.

19. FREEDMAN, D. A. and FIENBERG, S. (Feb. 1983, revised April 1983). Statistics and the scientific method, Commentson and reactions to Freedman, A rejoinder to Fienberg's comments. Springer New York 1985 Cohort Analysis in SocialResearch, (W. M. Mason and S. E. Fienberg, eds.).

20. FREEDMAN, D. A. and PETERS, S. C. (March 1983, revised Jan. 1984). Using the bootstrap to evaluate forecastingequations. J. of Forecasting. 1985, Vol. 4, 251-262.

21. FREEDMAN, D. A. and PETERS, S. C. (March 1983, revised Aug. 1983). Bootstrapping an econometric model: someempirical results. JBES, 1985, 2, 150-158.

22. FREEDMAN, D. A. (March 1983). Structural-equation models: a case study.

23. DAGGETT, R. S. and FREEDMAN, D. (April 1983, revised Sept. 1983). Econometrics and the law: a case study in theproof of antitrust damages. Proc. of the Berkeley Conference, in honor of Jerzy Neyman and Jack Kiefer. Vol I pp.123-172. (L. Le Cam, R. Olshen eds.) Wadsworth, 1985.

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24. DOKSUM, K. and YANDELL, B. (April 1983). Tests for exponentiality. Handbook of Statistics, (P. R. Krishnaiah andP. K. Sen, eds.) 4, 1984.

25. FREEDMAN, D. A. (May 1983). Comments on a paper by Markus.

26. FREEDMAN, D. (Oct. 1983, revised March 1984). On bootstrapping two-stage least-squares estimates in stationary linearmodels. Anm. S 1984, 12,827-842.

27. DOKSUM, K. A. (Dec. 1983). An extension of partial likelihood methods for proportional hazard models to generaltransfornation models. Ann. Statist., 1987, 15, 325-345.

28. BICKEL, P. J., GOETZE, F. and VAN ZWET, W. R. (Jan. 1984). A simple analysis of third order efficiency of estimateProc. of the Neyman-Kiefer Conference, (L. Le Cam, ed.) Wadsworth, 1985.

29. BICKEL, P. J. and FREEDMAN, D. A. Asymptotic normality and the bootstrap in stratified sampling. Amn. Statist.12 470-482.

30. FREEDMAN, D. A. (Jan. 1984). The mean vs. the median: a case study in 4-R Act litigation. JBES. 1985 Vol 3pp. 1-13.

31. STONE, C. J. (Feb. 1984). An asymptotically optimal window selection rule for kemel density estimates. Ann. Statist.,Dec. 1984, 12, 1285-1297.

32. BREIMAN, L. (May 1984). Nail finders, edifices, and Oz.

33. STONE, C. J. (Oct. 1984). Additive regression and other nonparametric models. Ann. Statist., 1985, 13, 689-705.

34. STONE, C. J. (June 1984). An asymptotically optimal histogram selection rule. Proc. of the Berkeley Conf. in Honor ofJerzy Neyman and Jack Kiefer (L Le Cam and R. A. Olshen, eds.), II, 513-520.

35. FREEDMAN, D. A. and NAVIDL W. C. (Sept. 1984, revised Jan. 1985). Regression models for adjusting the 1980Census. Statistical Science. Feb 1986, Vol. 1, No. 1, 3-39.

36. FREEDMAN, D. A. (Sept. 1984, revised Nov. 1984). De Finetti's theorem in continuous time.

37. DIACONIS, P. and FREEDMAN, D. (Oct. 1984). An elementary proof of Stirling's formula. Amer. Math Monthly. Feb1986, Vol. 93, No. 2, 123-125.

38. LE CAM, L. (Nov. 1984). Sur l'approximation de familles de mesures par des families Gaussiennes. Ann. Inst.Henri Poincar6, 1985, 21, 225-287.

39. DIACONIS, P. and FREEDMAN, D. A. (Nov. 1984). A note on weak star uniformities.

40. BRELMAN, L. and IHAKA, R. (Dec. 1984). Nonlinear discrimiinant analysis via SCALING and ACE.

41. STONE, C. J. (Jan. 1985). The dimensionality reduction principle for generalized additive models.

42. LE CAM, L. (Jan. 1985). On the nornal approximation for sums of independent variables.

43. BICKEL, P. J. and YAHAV, J. A. (1985). On estimating the number of unseen species: how many executions werethere?

44. BRILLINGER, D. R. (1985). The natural variability of vital rates and associated statistics. Biometrics, to appear.

45. BRILLINGER, D. R. (1985). Fourier inference: some methods for the analysis of array and nonGaussian series data.Water Resources Bulletin, 1985, 21, 743-756.

46. BREIMAN, L. and STONE, C. J. (1985). Broad spectrum estimates and confidence intervals for tail quantiles.

47. DABROWSKA, D. M. and DOKSUM, K. A. (1985, revised March 1987). Partial likelihood in transformation modelswith censored data.

48. HAYCOCK, K. A. and BRILLINGER. D. R. (November 1985). LIBDRB: A subroutine library for elementary timeseries analysis.

49. BRILLINGER, D. R. (October 1985). Fitting cosines: some procedures and some physical examples. Joshi Festschrift,1986. D. Reidel.

50. BRILLINGER, D. R. (November 1985). What do seismology and neurophysiology have in common? - Statistics!Comptes Rendus Math. Acad. Sci. Canada. January, 1986.

51. COX, D. D. and O'SULLIVAN, F. (October 1985). Analysis of penalized likelihood-type estimators with application togeneralized smoodting in Sobolev Spaces.

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52. O'SULLIVAN, F. (November 1985). A practical perspective on ill-posed inverse problems: A review with somenew developments. To appear in Journal of Statistical Science.

53. LE CAM, L. and YANG, G. L. (November 1985, revised March 1987). On the preservation of local asymptotic normalityunder information loss.

54. BLACKWELL D. (November 1985). Approximate normality of large products.

55. FREEDMAN, D. A. (June 1987). As others see us: A case study in path analysis. Joumal of EducationalStatistics. 12, 101-128.

56. LE CAM, L. and YANG, G. L. (January 1986). Replaced by No. 68.

57. LE CAM, L. (February 1986). On the Bernstein - von Mises theorem.

58. O'SULLIVAN, F. (January 1986). Estimation of Densities and Hazards by the Method of Penalized likelihood.

59. ALDOUS, D. and DIACONIS, P. (February 1986). Strong Uniform Times and Finite Random Walks.

60. ALDOUS, D. (March 1986). On the Markov Chain simulation Method for Unifonn Combinatorial Distributions andSimulated Annealing.

61. CHENG, C-S. (April 1986). An Optimization Problem with Applications to Optimal Design Theory.

62. CHENG, C-S., MAJUMDAR, D., STUFKEN, J. & TURE, T. E. (May 1986, revised Jan 1987). Optimal step typedes'gn for comparing test treatments with a control.

63. CHENG, C-S. (May 1986, revised Jan. 1987). An Application of the Kiefer-Wolfowitz Equivalence Theorem.

64. O'SULLIVAN, F. (May 1986). Nonparametric Estimation in the Cox Proportional Hazards Model.

65. ALDOUS, D. (JUNE 1986). Finite-Time Implications of Relaxation Times for Stochastically Monotone Processes.

66. PrTMAN, J. (JULY 1986, revised November 1986). Stationary Excursions.

67. DABROWSKA, D. and DOKSUM, K. (July 1986, revised November 1986). Estimates and confidence intervals formedian and mean life in the proportional hazard model with censored data.

68. LE CAM, L. and YANG, G.L. (July 1986). Distinguished Statistics, Loss of information and a theorem of Robert B.Davies (Fourth edition).

69. STONE, C.J. (July 1986). Asymptotic properties of logspline density estimation.

71. BICKEL, P.J. and YAHAV, J.A. (July 1986). Richardson Extrapolation and the Bootstrap.

72. LEHMANN, E.L. (July 1986). Statistics - an overview.

73. STONE, C.J. (August 1986). A nonparametric framework for statistical modelling.

74. BIANE, PH. and YOR, M. (August 1986). A relation between L6vy's stochastic area formula, Legendre polynomial,and some continued fractions of Gauss.

75. LEHMANN, E.L. (August 1986, revised July 1987). Comparing Location Experiments.

76. O'SULLIVAN, F. (September 1986). Relative risk estimation.

77. O'SULLIVAN, F. (September 1986). Deconvolution of episodic hormone data.

78. PITMAN, J. & YOR, M. (September 1987). Further asymptotic laws of planar Brownian motion.

79. FREEDMAN, D.A. & ZEISEL, H. (November 1986). From mouse to man: The quantitative assessment of cancer risks.To appear in Statistical Science.

80. BRILLINGER, D.R. (October 1986). Maximum likelihood analysis of spike trains of interacting nerve cells.

81. DABROWSKA, D.M. (November 1986). Nonparametric regression with censored survival time data.

82. DOKSUM, K.J. and LO, A.Y. (November 1986). Consistent and robust Bayes Procedures for Location based onPartial Infonnation.

83. DABROWSKA, D.M., DOKSUM, KA. and MIURA, R. (November 1986). Rank estimates in a class of semiparametrictwo-sample models.

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84. BRILLINGER, D. (Deember 1986). Some statistical methods for random process data from seismology andneurophysiology.

85. DIACONIS, P. and FREEDMAN, D. (December 1986). A dozen de Finetti-style results in search of a theory.Ann. Inst. Henri Poincar, 1987, 23, 397-423.

86. DABROWSKA, D.M. (January 1987). Uniform consistency of nearest neighbour and kemel conditional Kaplan- Meier estimates.

87. FREEDMAN, DA., NAVIDI, W. and PETERS, S.C. (February 1987). On the impact of variable selection infitting regression equations.

88. ALDOUS, D. (February 1987, revised April 1987). Hashing with linear probing, under non-uniform probabilities.

89. DABROWSKA, D.M. and DOKSUM, K.A. (March 1987, revised January 1988). Estimating and testing in a twosample generalized odds rate model.

90. DABROWSKA, D.M. (March 1987). Rank tests for matched pair experiments with censored data.

91. DIACONIS, P and FREEDMAN, D.A. (April 1988). Conditional limit theorems for exponential families and finiteversions of de Finetti's theorem. To appear in the Journal of Applied Probability.

92. DABROWSKA, D.M. (April 1987, revised September 1987). Kaplan-Meier estimate on the plane.

92a. ALDOUS, D. (April 1987). The Harmonic mean formula for probabilities of Unions: Applications to sparse randomgraphs.

93. DABROWSKA, D.M. (June 1987, revised Feb 1988). Nonparametric quantile regression with censored data.

94. DONOHO, D.L. & STARK, PJB. (June 1987). Uncertainty principles and signal recovery.

95. CANCELLED

96. BRILLINGER, D.R. (June 1987). Some examples of the statistical analysis of seismological data. To appear inProceedings, Centennial Anniversary Symposium, Seismographic Stations, University of California, Berkeley.

97. FREEDMAN, DA. and NAVIDI, W. (June 1987). On the multi-stage model for carcinogenesis. To appear inEnvirormental Health Perspectives.

98. O'SULLIVAN, F. and WONG, T. (June 1987). Determining a function diffusion coefficient in the heat equation.99. O'SULLIVAN, F. (June 1987). Constrained non-linear regularization with application to some system identification

problems.

100. LE CAM, L. (July 1987, revised Nov 1987). On the standard asymptotic confidence ellipsoids of Wald.

101. DONOHO, D.L. and LIU, R.C. (July 1987). Pathologies of some minimum distance estimators. Annals ofStatistics, June, 1988.

102. BRILLINGER, D.R., DOWNING, K.H. and GLAESER, R.M. (July 1987). Some statistical aspects of low-doseelectron imaging of crystals.

103. LE CAM, L. (August 1987). Harald Cramer and sums of independent random variables.

104. DONOHO, A.W., DONOHO, D.L. and GASKO, M. (August 1987). Macspin: Dynamic graphics on a desktopcomputer. IEEE Computer Graphics and applications, June, 1988.

105. DONOHO, D.L. and LIU, R.C. (August 1987). On minimax estimation of linear functionals.

106. DABROWSKA, D.M. (August 1987). Kaplan-Meier estimate on the plane: weak convergence, LIL and the bootstrap.

107. CHENG, C-S. (August 1987). Some orthogonal main-effect plans for asymmetrical factorials.

108. CHENG, C-S. and JACROUX, M. (August 1987). On the construction of trend-free run orders of two-level factorialdesigns.

109. KLASS, M.J. (August 1987). Maximizing E max S / ES': A prophet inequality for sums of I.I.D. mean zero variates.

110. DONOHO, D.L. and LIU, R.C. (August 1987). The "automatic" robustness of minimum distance functionals.Armals of Statistics, June, 1988.

111. BICKEL P.J. and GHOSH, J.K. (August 1987, revised June 1988). A decomposition forte likelihood ratio statisticand the Bartlett correction- a Bayesian argument.

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112. BURDZY, K., PiTMAN, J.W. and YOR, M. (September 1987). Some asymptotic laws for crossings and excursions.

113. ADHIKARI, A. and P1TMAN, J. (September 1987). The shortest planar arc of width 1.

114. RITOV, Y. (September 1987). Estimation in a linear regression model with censored data.

115. BICKEL, P.J. and RITOV, Y. (SepL 1987, revised Aug 1988). Large sample theory of estimation in biased samplingregression models I.

116. RITOV, Y. and BICKEL, P.J. (Sept.1987, revised Aug. 1988). Achieving information bounds in non andsemiparametric models.

117. RITOV, Y. (October 1987). On the convergence of a maximal correlation algorithm with alternating projections.

118. ALDOUS, D.J. (October 1987). Meeting times for independent Markov chains.

119. HESSE, C.H. (October 1987). An asymptotic expansion for the mean of the passage-time distribution of integratedBrownian Motion.

120. DONOHO, D. and LIU, R. (October 1987, revised March 1988). Geometrizing rates of convergence, I1.

121. BRILLINGER, D.R. (October 1987). Estimating the chances of large earthquakes by radiocarbon dating and statisticalmodelling. To appear in Statistics a Guide to the Unknown.

122. ALDOUS, D., FLANNERY, B. and PALACIOS, J.L. (November 1987). Two applications of um processes: The fringeanalysis of search trees and the simulation of quasi-stationary distributions of Markov chains.

123. DONOHO, D.L., MACGIBBON, B. and LIU, R.C. (Nov.1987, revised July 1988). Minimax risk for hyperrectangles.

124. ALDOUS, D. (November 1987). Stopping times and tightness II.

125. HESSE, C.H. (November 1987). The present state of a stochastic model for sedimentation.

126. DALANG, R.C. (December 1987, revised June 1988). Optimal stopping of two-parameter processes onnonstandard probability spaces.

127. Same as No. 133.

128. DONOHO, D. and GASKO, M. (December 1987). Multivariate generalizations of the median and trimmed mean II.

129. SMITH, D.L. (December 1987). Exponential bounds in Vapnik-tervonenkis classes of index 1.

130. STONE, C.J. (Nov.1987, revised Sept. 1988). Uniform error bounds involving logspline models.

131. Same as No. 140

132. HESSE, C.H. (December 1987). A Bahadur - Type representation for empirical quantiles of a large class of stationary,possibly infinite - variance, linear processes

133. DONOHO, D.L. and GASKO, M. (December 1987). Multivariate generalizations of the median and trimmed mean, I.

134. DUBINS, L.E. and SCHWARZ, G. (December 1987). A sharp inequality for martingales and stopping-times.

135. FREEDMAN, D.A. and NAVIDI, W. (December 1987). On the risk of lung cancer for ex-smokers.

136. LE CAM, L. (January 1988). On some stochastic models of the effects of radiation on cell survival.

137. DIACONIS, P. and FREEDMAN, D.A. (April 1988). On the uniform consistency of Bayes estimates for multinomialprobabilities.

137a. DONOHO, D.L. and LIU, R.C. (1987). Geometrizing rates of convergence, I.

138. DONOHO, D.L. and LIU, R.C. (January 1988). Geometrizing rates of convergence, HI.

139. BERAN, R. (January 1988). Refining simultaneous confidence sets.

140. HESSE, C.H. (December 1987). Numerical and statistical aspects of neural networks.

141. BRILLINGER, D.R. (January 1988). Two reports on trend analysis: a) An Elementary Trend Analysis of Rio NegroLevels at Manaus, 1903-1985 b) Consistent Detection of a Monotonic Trend Superposed on a Stationary Time Series

142. DONOHO, D.L. (Jan. 1985, revised Jan. 1988). One-sided inference about functionals of a density.

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143. DALANG, R.C. (February 1988). Randomization in the two-armed bandit problem.144. DABROWSKA, D.M., DOKSUM, KA. and SONG, J.K. (February 1988). Graphical comparisons of cumulative hazards

for two populations.145. ALDOUS, D.J. (February 1988). Lower bounds for covering times for reversible Markov Chains and random walks on

graphs.146. BICKEL, P.J. and RITOV, Y. (Feb.1988, revised August 1988). Estimating integrated squared density derivatives.

147. STARK, P.R. (March 1988). Strict bounds and applications.

148. DONOHO, D.L. and STARK, P.B. (March 1988). Rearrangements and smoothing.

149. NOLAN, D. (March 1988). Asymptotics for a multivariate location estimator.

150. SEILLEER, F. (March 1988). Sequential probability forecasts and the probability integral transfonn.

151. NOLAN, D. (March 1988). Limit theorems for a random convex set.

152. DIACONIS, P. and FREEDMAN, DA. (April 1988). On a theorem of Kuchler and Lauritzen.

153. DIACONIS, P. and FREEDMAN, D.A. (April 1988). On the problem of types.

154. DOKSUM, KA. (May 1988). On the correspondence between models in binary regression analysis and survival analysis.

155. LEHMANN, E.L. (May 1988). Jerzy Neyman, 1894-1981.

156. ALDOUS, D.J. (May 1988). Stein's method in a two-dimensional coverage problem.

157. FAN, J. (June 1988). On the optimal rates of convergence for nonparametric deconvolution problem.

158. DABROWSKA, D. (June 1988). Signed-rank tests for censored matched pairs.

159. BERAN, R.J. and MILLAR, P.W. (June 1988). Multivariate symmetry models.

160. BERAN, R.J. and MILLAR, P.W. (June 1988). Tests of fit for logistic models.

161. BREIMAN, L. and PETERS, S. (June 1988). Comparing automatic bivariate smoothers (A public service enterprise).

162. FAN, J. (June 1988). Optimal global rates of convergence for nonparametric deconvolution problem.

163. DIACONIS, P. and FREEDMAN, DA. (June 1988). A singular measure which is locally uniform.

164. BICKEL, P.J. and KREEGER, A.M. (July 1988). Confidence bands for a distribution function using the bootstrap.

165. HESSE, C.H. (July 1988). New methods in the analysis of economic time series I.

166. FAN, JIANQING (July 1988). Nonparametric estimation of quadratic functionals in Gaussian white noise.

167. BREIMAN, L., STONE, C.J. and KOOPERBERG, C. (August 1988). Confidence bounds for extreme quantiles.

168. LE CAM, L. (August 1988). Maximum likelihood an introduction.

169. BREIMAN, L. (August 1988). Submodel selection and evaluation in regression-The conditional caseand little bootstrap.

170. LE CAM, L. (September 1988). On the Prokhorov distance between the empirical process and the associated Gaussianbridge.

171. STONE, C.J. (September 1988). Large-sample inference for logspline models.

172. ADLER, R.J. and EPSTEIN, R. (September 1988). Intersection local times for infinite systems of planar brownianmotions and for the brownian density process.

173. MILLAR, P.W. (October 1988). Optimal estimation in the non-parametric multiplicative intensity model.

174. YOR, M. (October 1988). Interwinings of Bessel processes.

175. ROJO, J. (October 1988). On the concept of tail-heaviness.

Copies of these Reports plus the most recent additions to the Technical Report series are available from the StatisticsDepartment technical typist in room 379 Evans Hall or may be requested by mail from:

Department of StatisticsUniversity of CalifomiaBerkeley, Califomia 94720

Cost: $1 per copy.