Estimation of parameters for normally distributed random matrices

Abstract Consider the p × n random matrix X which is normally distributed with mean M , and let the covariance matrix between any two columns of X (say x i and x j ) be γ ij (Σ+Σ ϵ ). Expectations and convariances of the maximum likelihood estimators of M and Σ are given for the situation when γ ij and Σ ϵ are known.