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An adjustment by which the sample means of several variables are compressed toward the grand mean of those variables. For example, if two variables have sample means of 10% and 20%, they can be compressed toward the grand mean of 15% by weighting the sample means by 70% and the grand mean by 30%. In this example, the adjusted means would equal 11.5% and 18.5%, respectively. The optimal weighting scheme is a function of the size of the samples used to derive the original estimates. The Bayes Stein procedure is often used in optimization applications to reduce the sensitivity of the results to errors in the parameter estimates.
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