In this paper, maximum likelihood estimators for a broad class of matr
ix variate elliptically contoured distributions have been derived. Opt
imality properties of estimators in the multivariate regression models
are studied when the error term has a matrix variate elliptically con
toured distribution. Least-square estimators are also obtained for the
multivariate random effect regression model when the underlying distr
ibution is elliptically contoured.