Risk behavior of variance estimators in multivariate normal distribution

Abstract

In this paper we consider the estimation problem of unknown variance of a multivariate normal vector under quadratic loss and entropy loss. The behavior of risk functions of the Brewster--Zidek estimator and the original Stein estimator is examined. Numerical studies show that an asymptotically inadmissible Stein estimator provides a larger degree of improvement than an admissible Brewster--Zidek estimator.Variance estimation quadratic loss entropy loss Brewster--Zidek estimator Stein estimator confluent hypergeometric function