Maximum likelihood estimation for multivariate normal samples : theory and methods

Abstract

Maximum likelihood estimation of parameter structures in the case of multivariate normal samples is considered. The procedure provides a new statistical methodology for maximum likelihood estimation which does not require derivation and solution of the likelihood equations. It is a flexible procedure for the analysis of specific structures in mean vectors and covariance matrices – including the case where the sample size is small relative to the dimension of the observations. Special cases include different variations of the Behrens-Fisher problem, proportional covariancematrices and proportional mean vectors. Specific structures are illustrated with real data examples.