A maximum likelihood algorithm for the mean and covariance of nonidentically distributed observations

An iterative procedure for computing the maximum likelihood estimates of the mean and the covariance of a normal random vector, based on nonidentically distributed observations, is developed. The procedure is derived from the general theory of EM algorithm. It is shown that the evaluation of the gradient and Hessian is not necessary for this procedure. The algorithm can also be applied to the case in which some parameters are constrained to known values. Some examples are examined to show the computational efficiency of this algorithm.