SIMULTANEOUS ESTIMATION OF SCALE MATRICES IN TWO-SAMPLE PROBLEM UNDER ELLIPTICALLY CONTOURED DISTRIBUTIONS

Abstract

Two-sample problems of estimating p × p scale matrices are investigated under elliptically contoured distributions. Two loss functions are employed; one is sum of Stein’s loss functions of one-sample problem of estimating a normal covariance matrix and the other is a quadratic loss function for Σ2Σ −1 1 , where Σ1 and Σ2 are p × p scale matrices of elliptically contoured distribution models. It is shown that improvement of the estimators obtained under the normality assumption remains robust under elliptically contoured distribution models. A Monte Carlo study is also conducted to evaluate the risk performances of the improved estimators under three elliptically contoured distributions.