IMPROVED ESTIMATION OF PARAMETER MATRICES IN A ONE-SAMPLE AND TWO-SAMPLE PROBLEMS

PUI LAM LEUNG AND FOON YIP NG

Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, China

(Received October 19, 1999; revised July 14, 2000)

Abstract. In this paper, the problems of estimating the covariance matrix in a Wishart distribution (refer as one-sample problem) and the scale matrix in a multivariate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their harmonic mean is proposed. It is shown that the new estimator dominates the best linear estimator under two scale invariant loss functions.

Key words and phrases: Covariance matrix, orthogonally invariant estimator, decision– theoretic estimation, shrinkage estimator, harmonic mean, eigenvalues.