Shrinkage preliminary test estimation in multivariate normal distributions

Abstract

To estimate the mean vector of a multivariate normal distribution , a random sample of size n 1is used. Suppose a second independent random sample of size n 2from is available and it is a priori suspected that μ (1) = μ (2) may hold. We propose a shrinkage preliminary test estimate (SPTE) mean vector μ (1) that may be viewed as a preliminary test estimator improving the usual one given by Ahmed (1987). This proposed estimator is superior in bias and efficiency to the usual preliminary test estimator (PTE). Furthermore, it dominates the classical estimator in a range that is wider than that of the usual preliminary estimator. The size of the preliminary test for SPTE is much more appropriate .than the PTE.