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

Two-sample problems of estimating p × p scale matrices are investigated under elliptically contoured distributions. Two loss functions are employed ; one is the sum of Stein's loss functions of the one-sample problem of estimating a normal covariance matrix and the other is a quadratic loss function for Σ_2Σ^<-1>_1, where Σ_1 and Σ_2 are p × p scale matrices of elliptically contoured distributions. It is shown that improvement of the estimators obtained under the normality assumption remains robust under elliptically contoured distributions. A Monte Carlo study is also conducted to evaluate the risk performances of the improved estimators under three elliptically contoured distributions.