Estimation of the mean and the covariance matrix under a marginal independence assumption — an application of matrix differential calculus Original Research Article

The estimation of the mean and the covariance matrix of a normal population has been investigated in the literature under various assumptions. We consider minimum distance estimation of the parameters w.r.t. the Kullback-Leibler distance under a marginal independence assumption. Namely, the subvectors xL and xK are supposed to be independent when the underlying random vector x is partitioned like (x′L, x′K, x′R)′. In this setting we derive 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. Furthermore, we consider maximum likelihood estimation of the correlation matrix when only the sample correlation matrix is available.