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Deming's statistical consulting advice to us is rich and varied. I knew Deming a little and long loved him from afar. That affection for this great man should be evident in this talk. To give focus to my remarks, in this lecture I will cover just one of his quality ideas in depth. This is the algorithm commonly called "raking."
Raking, or raking ratio estimation, was advanced by Deming and Stephan for use in the 1940 U.S. Decennial Census. The algorithm employs at its heart a process whereby the weights of a data set are iteratively ratioed-adjusted within categories, until they simultaneously meet, within tolerance, a set of pre-specified population totals.
Some confusion surrounded raking's introduction slowed its development. At its base the approach was intuitive. Its theoretical development came long after and some of the justifications for its use were misplaced, including by Deming.
For a long time the lack of computing power limited raking to modest applications and, given the work needed, the benefit/cost ratio often seemed insufficient relative to the time and money that had to be expended. These limitations no longer hold.
The problem of variance calculation accounting for raking posed additional challenges. These were solvable asymptotically in some decennial and sample survey settings; but usually not in a closed form. Even now, for general sample survey settings, replication techniques are most commonly the only practical solution available.
Today's talk will motivate these assertions with some examples taken from my practice and that of other statisticians. Extensions by me to multivariate raking will also be covered and speculations on some unsolved or incompletely posed problems will be offered. Throughout I will intersperse examples from my decades of practice.
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