Rake’s Progress Revisited

Nada Ganesh and Fritz ScheurenWSS

September 24, 2014

Snacks and Knacks• About the Talk Title?• Application History First!• Information Theory too?• Raking’s Roles in Surveys?• Some Examples (Handout)?• More Snacks and Knacks?• Wraps and Conjectures!

Why Call Algorithm Raking?

• Maybe a Lofty Origin?• Perhaps a 1951 opera by

Stravinsky inspired by 1733-5 engravings by Hogarth• Or maybe a Humbler Origin!• The Dairy Farm Rake?• What is Your Guess?

Basic Raking Algorithm

• Repeated Ratio-ing “r’ of a (Weighted) sample total “t” to a control total “T as in “r=T/t”• Total by Total repeatedly until all

the adjusted sample totals “t” were as close as wanted to “T”

Application History First!

• The Pre-1940 Period• The 1940 Deming-Stephan AMS

Paper to align Survey/Census• Not Widely used in 1940 Census?

Because of WWII!• Regularly Forgotten/Recovered

Information Theory too?

• Kullback “Kully” and Ireland “Terry’s”Proof of Convergence• From Calculus a Bounded

Monotonic Series Converges• Information Theory Affirms this• When Constraints are Consistent

Raking’s Roles in Surveys?

• Aligning to Agreed upon Control totals – aka Calibration

-- Variance reduction -- Bias Correction MSE?• Hand-waving but Maybe harmful

Sometimes because unit based

More Snacks and Knacks?

• Convergence Practices and Possible Improvements• Variable Bounds on Dimensions• Iterating Worst Dimensions First• Early/Differential Stopping Rules• “Family” Harmonic Adjustments

More Application Settings • Chip Alexander and CPS/ACS• Survey and Administrative Linked

Files (CPS/IRS/SSA)• File Alignment before Raking?• Reducing Impact on Linkage Errors

(Maybe both Variance/Bias)

Two Examples

• Geometric Family Weight Example (Ganish)• Changing Convergence

Algorithm to Quicken Speed (Ganish)• Role for Synthetic Estimation

(Phil?)

Wraps and Conjectures!

• A Multi-Use Tool, Like Pliers• Computational Barriers long

since gone • More work on Diagnostics

needed though• More work on multiple weights

Many, Many, Many Thanks