Estimation of the mean and the covariance matrix under a marginal independence assumption - an application of matrix differential calculus

The estimation of the mean and the covariance matrix of a normal population has been investigated in the literature under various assumptions. We cons ider minimum distance estimation of the parameters w.r.t. the Kullback-Leib ler distance under a marginal independence assumption. Namely, the subvecto rs x(L) and x(K) are supposed to be independent when the underlying random vector x is partitioned like (x(L)', x(K)', x(R)')'. In this setting we der ive two different estimators of the covariance matrix of x. In particular, this approach includes maximum likelihood estimation. The derivation of the estimator proceeds by the method of matrix differential calculus. Furtherm ore, we consider maximum likelihood estimation of the correlation matrix wh en only the sample correlation matrix is available. (C) 1999 Elsevier Scien ce Inc. All rights reserved.