Pitman's closeness criterion and shrinkage estimates of the variance and the S.D.

Abstract

Pitman’s closeness criterion (PCC) became a controversial topic since some statisticians expressed their wish to exclude it from the evaluation criteria of estimates. Herein, PCC is studied for an estimate t and its shrinkage ct, when the unknown parameter of interest is positive; 0 < c < 1. PCC is transitive for shrinkage estimates with decreasing shrinkage coefficients and only t’s distribution is needed to compute its value. When is the variance 2 or the standard deviation , exact calculations and simulations confirm that ct, which improves t’s mean square error, may not improve often t’s distance from and PCC takes large values. Consequently, some statisticians, their clients and some statistics’ users will not use shrinkage estimates of 2 and of . For this group, PCC is a useful information tool to be used along with other evaluation criteria, as suggested by Rao (1993).