On Double-Stage Estimation of the Mean Using Prior Knowledge

Abstract

SUMMARY A double-sample procedure is considered for lowering the mean squared error for the estimator of the mean in a region R around a prior estimate 0o. The proposed two-stage scheme is as follows: we obtain a sample of size n1 and compute 01, the minimum variance unbiased estimator of 0. If 01 ? R, where R = [o - co-, so + co], we use a technique for shrinking 01 toward the initial estimate 0o. If O' I R, we take another sample of size n2, calculate 02, and then pool 01 and 02. Hence the double-stage shrinkage (DSS) estimator is given by