Combining Estimates of Location

Abstract

Suppose we are given independent random samples of size m and n, respectively, on two populations with the same density, same location parameter, but different scale parameter. Let and denote odd location-scale estimators of location based on the individual samples. If the density is bounded and symmetric about the location parameter, under further very mild conditions, a combined estimator is found which is unbiased and has smaller variance than , for m ≥ 2, n ≥ 6. Values of m and n are indicated for which the usual combined estimator has smaller variance than either or . Details are worked out for the rectangular distribution.