Shrinkage preliminary test estimation in multivariate normal distributions

摘要

To estimate the mean vector of a multivariate normal distribution, a random sample of sizen1is used. Suppose a second independent random sample of sizen2fromis available and it isa priorisuspected that#x3BC;(1)=#x3BC;(2)may hold. We propose ashrinkage preliminary test estimate (SPTE) mean vector#x3BC;(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 usualpreliminary 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 forSPTEis much more appropriate .than thePTE.