1089J. Rojo (ed.), Selected Works of E. L. Lehmann, Selected Works in Probability and Statistics, DOI 10.1007/978-1-4614-1412-4_93, © Springer Science+Business Media, LLC 2012

The Books

Javier Rojo

As a young man, Eric Leo Lehmann had a desire to become a writer. In Lehmann (2008), he writes that "My passion was German literature, my dream to become a writer, perhaps another Thomas Mann or Gottfried Keller." But the Nazis had come to power in 1933, and his father had decided to take the family to Zurich. Now, two years later, Erich's father advises him to consider other options as it will be impossible to return to Germany. Perhaps mathematics, with a universal character, would be a good choice. It happened that Edmund Landau's wife was a good friend of Erich's mother. Erich's father thought that Landau should be consulted on Erich's mathematical ability. For this purpose, Landau was invited to visit in his next trip to Zurich. After a two hour session with Erich, Landau recommended to his parents that mathematics could be an option. Realizing that Switzerland was not a good place for a German refugee, and seeking and then following Landau's advice once more, Erich went to England and enrolled in Trinity College. After two years, and with a letter of introduction for Courant from Landau's wife -Landau had passed away earlier from a heart attach, Erich arrived in New York. After being asked if he wanted to live in the United States or in New York, and having preferred the former, Courant recommends Berkeley as "an up-and-coming university" that will be a good place for Erich. And so it happened that Erich Leo Lehmann arrived in Berkeley in 1941.

Griffith C. Evans, who had been recruited from the Rice Institute - now Rice University-, was the chair of the Mathematics Department at Berkeley. Evans moved to Berkeley to build up the Mathematics Department which was in a bit of a disarray. Evans had a broad vision of Mathematics that included Statistics. Fisher was invited to visit Berkeley as a way to preview a possible association with Berkeley. Reid (1982) writes that Evans " ... had become personally acquainted with Fisher during summer weeks they had spent together at the University of Michigan in 1931". In addition, Reid (1982) continues, in a set of notes, "A Brief History of the Mathematics

J. Rojo Professor of Statistics, Department of Statistics, Rice University, Houston, TX 77005 e-mail : jrojo@rice.edu

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Department", Evans writes that he considered California "as the place for a really outstanding statistician, if possible of the level of R. A. Fisher himself'. Fisher's visit, however, did not go well. But Evans persevered in his efforts to build up statistics within the mathematics department. Although he did not know Neyman, word got to him about the success of Neyman's rounds of visits to several universities (e.g., Columbia, Princeton, Chicago) that culminated with a very successful visit to the U.S. Department of Agriculture. Without knowing him, Evans offered Neyman a position. These details as well as Erich's interactions with Evans and Neyman have been fascinatingly described in Lehmann (2008) and Reid (1982).

But it was, very likely, the early passion for writing that led Erich to write several successful and influential books. The list includes:

1. Testing statistical hypotheses. First edition, 1959. Second edition, 1986. Third edition, with Joseph P. Romano, 2005. The first edition has been translated into Russian (1964), Polish (1968), and Japanese.

2. Basic Concepts of Probability and Statistics, with Joseph L. Hodges. First edition 1964. Reprinted in 2005 as part of the SIAM series Classics in Applied Mathematics. Second edition 1970. This book has been translated into Hebrew (1972), Farsi (1994), Italian (1971), and Danish (1969).

3. Elements of Finite Probability, with Joseph L. Hodges. First edition 1965. Second edition 1970.

4. Nonparametrics: Statistical Methods Based on Ranks, with the assistance of H. J. M. D' Abrera. First published as a hardcover by Holden-Day in 1975. In paperback by Prentice-Hall, Inc., Simon & Schuster in 1998, and then by Springer Science+ Business Media, LLC in 2006. The book has been translated into Japanese (1998).

5. Theory of Point Estimation. First edition, 1983. Second edition, with George Casella, 1998. The first edition was translated into Russian (1991 ), and the second into Chinese (2004 ).

6. Elements of Large-Sample Theory, 1999. 7. Reminiscences of a Statistician: The Company I Kept, 2008.

In addition, Lehmann was a Special Editor for the second edition of Statistics: A Guide to the Unknown, edited by Judith M. Tanur. There were two printings of this second edition: the original edition was published in 1978 and it has been translated into Chinese (1980) and Spanish (1992). The second printing was published in 1985. For the third edition, published in 1989, Judith M. Tanur was the editor while Lehmann continued as a co-editor. He was joined by Frederick Mosteller, William H. Kruskal, Richard F. Link, Richard S. Pieters and Gerald R. Rising. Two more works, Statistics: a guide to the study of the biological and health sciences and Statistics: a guide to political and social issues, both published in 1977, were a result of this group's collaborative efforts. Lehmann was a Special Editor for the latter and a co-editor for the former.

At the time of his death, Erich was working on a manuscript for a new book soon to be published by Springer-Verlag. The title of the book is Fisher, Neyman, and the Creation of Classical Statistics. After his death, Juliet Shaffer has been working

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diligently to bring the book to its final form for publication. In addition, Lehmann was collaborating with Fritz Scholz on a revision of the Nonparametrics: Statistical Methods Based on Ranks book that will incorporate the usage of R. At the time of this writing, Fritz continues his indefatigable efforts on the revision and plans to have the book out in approximately two years.

Testing Statistical Hypotheses (TSH) and Theory of Point Estimation (TPE) have been the most influential of Erich's books. These books have been a mainstay in many Ph.D. programs, helping to educate future generations of statisticians. The genesis of the first edition of TSH has been discussed in Lehmann ( 1997), and the preface of the first edition of TPE gives a glimpse of how the book evolved. In both cases, Colin Blyth played an important role in facilitating the gestation of these books.

Several reviews of these books have appeared in the literature. For a review of Lehmann (1959) see, e.g. Pratt (1961); for a review of Lehmann and Romano (2005) see, e.g. Steinebach (2006). For a review of Hodges and Lehmann ( 1964 ), see Hedayat (1970); Grum (2006) reviewed the 2nd edition. Gastwirth (1977) reviewed Lehmann (1975). Rao (1984), Bickel (1984), and Berger (1984), reviewed TPE, F 1 edition. Strawderman (2000) reviewed TPE, 2nd edition. Finally, Bellhouse (2008) reviewed Lehmann (2008).

The review by Speed (2008) on Reminiscences of a Statistician: The Company I Kept, and the review by Holmes (2000) on Elements of Large-Sample Theory are reproduced in this chapter.

In addition, George Casella and Joseph Romano provide fascinating accounts on their collaboration with Erich on the second and third editions of TPE and TSH, respectively. Finally, Doug Wolfe reviews the impact that Nonparametrics: Statistical Methods Based on Ranks had, and continues to have, on the discipline and on him personally.

References

[1] Bellhouse, D. (2008). Review of Reminiscences of a Statistician: The Company I Kept by Erich L. Lehmann. Mathematical reviews, MR2367933 (2008k:01021).

[2] Berger, J. 0. (1984). Review of Theory of Point Estimation, by E. Lehmann. Journal of the American Statistical Association, 79, 941-942.

[3] Bickel, P. J. (1984 ). Review of Theory of Point Estimation, by E. Lehmann. Metrika, 31, Number 1, 253-258.

[4] Bose, A. (1999) Review of Elements of Large-Sample Theory. Sankhya A, The Indian Journal of Statistics, 61, No. 3, 453-455.

[5] Bose, A. (2005). Review of Testing Statistical Hypothesis 3rd edition. Sankhya A. The Indian Journal of Statistics, 67, No. 4, 795-796.

[6] Gastwirth, J. L. (1977). Review of E. L. Lehmann, Nonparametrics: Statistical methods based on ranks. Bull. Amer. Math. Soc., 83, 967-973.

[7] Grum, J. (2006). Review of Basic Concepts of Probability and Statistics, by J.L. Hodges, Jr. and E.L. Lehmann. 2nd Ed. SIAM series Classics in Applied Mathematics. International Journal of Materials and Product Technology, 27, 295 - 295.

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[8] Hedayat, S. (1970). Book Review: Basic Concepts of Probability and Statistics, 2nd edition, by J. L. Hodges, Jr. and E. L. Lehman, Biometrics, 26, 589-590.

[9] Holmes, S. P. (2000). Review of Elements of Large-Sample Theory. Journal of the American Statistical Association, 95, 328-329.

[10] Lehmann, E. L. (1959). Testing Statistical Hypotheses. John Wiley & Sons, New York. [ 11] Lehmann, E. L., and Hodges, J. L. (1964 ). Basic Concepts of Probability and Statistics. Holden­

Day, Inc., San Francisco, London, Amsterdam. Reprinted in 2005 as part of the SIAM series Classics in Applied Mathematics.

[12] Lehmann, E. L. (1975). Nonparametrics: Statistical Methods Based on Ranks, with the assistance of H. J. M. D' Abrera. First published as a hardcover by Holden-Day in 1975. In paperback by Prentice-Hall, Inc., Simon & Schuster in 1998, and then by Springer Science+ Business Media, LLC in 2006.

[13] J. M. Tanur, F. Mosteller, W. H. Kruskal, E. L. Lehmann, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors (1977). Statistics: a guide to the study of the biological and health sciences. Holden-Day, Inc., Publishers, San Francisco, 140 pp.

[14] J. M. Tanur (Editor), E. L. Lehmann (Special Editor), F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors ( 1977). Statistics: a guide to political and social issues. Holden-Day, Inc., Publishers, San Francisco, 141 pp.

[15] J. M. Tanur (Editor), E. L. Lehmann (Special Editor), F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors (1978). Statistics: A Guide to the Unknown, Second Edition, Holden-Day, San Francisco.

[16] Lehmann, E. L. (1983). Theory of Point Estimation. Wiley & Sons, New York. Transferred to Wadsworth & Brooks/Cole 1991.

[17] J. M. Tanur (Editor), E. L. Lehmann (Special Editor), F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors (1985). Reprint of Statistics: A Guide to the Unknown, Second Edition, Wadsworth & Brooks/Cole.

[18] J. M. Tanur, F. Mosteller, W. H. Krusal, E. L. Lehmann, R. F. Link, R. S. Pieters, G. R. Rising, Co-editors. Statistics: A Guide to the Unknown, Third Edition. Wadsworth, 1989.

[19] J. M. Tanur (Editor), E. L. Lehmann (Special Editor), F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors. Chinese Translation of Statistics: A Guide to the Unknown, Second Edition, 1990.

[20] J. M. Tanur (Editor), E. L. Lehmann (Special Editor), F. Mosteller, W. H. Kruskal, R. F. Link, R. S. Pieters, and G. R. Rising, Co-editors. Spanish translation of Statistics: A Guide to the Unknown, Second Edition. Alianza Editorial, S. A., Spain, ISBN 842069651X, 1992.

[21] Lehmann, E. L. (1986). Testing Statistical Hypotheses, second edition. John Wiley & Sons, New York. Transferred to Wadsworth & Brooks/Cole, 1991.

[22] Lehmann, E. L. (1997). Testing Statistical Hypotheses: The Story of a Book. Statistical Science, 12, No. 1, 48-52.

[23] Lehmann, E. L., and Romano, J. P. (2005). Testing Statistical Hypotheses, third edition. Springer­Verlag, New York.

[24] Lehmann, E. L. (2008). Reminiscences of a Statistician: The Company I Kept. Springer-Verlag, New York.

[25] Pratt, J. W. (1961 ). Review of Testing Statistical Hypotheses by E. L. Lehmann. J. Amer. Statist. Ass. , 56, 163-167.

[26] Rao, C. R. (1984). Review of Theory of Point Estimation, by E. Lehmann. Journal of the American Statistical Association, 79, 942.

[27] Reid, C. (1982). Neyman from Life. Springer-Verlag, New York. [28] Speed, T. (2008). Review of Reminiscences of a Statistician: The Company I Kept by Erich

L. Lehmann. International Statistical Review, 76, 153. [29] Steinebach, J. (2006). Book Review: E. L. Lehmann, J.P. Romano: Testing Statistical Hypotheses

Springer New York 2005 (3rd edition), corr. 2nd printing 2006, XIV, 786 pages. Metrika, 64, 255-256.

[30] Strawderman, W. E. (2000). Review of Theory of Point Estimation (2nd ed.). E. L. Lehmann and George Casella. Journal of the American Statistical Association, 95, 329.