Minimax and admissible minimax estimators of the mean of a multivariate normal distribution for unknown covariance matrix

Let X be a p-variate (p >= 3) vector normally distributed with mean [mu] and covariance [Sigma], and let A be a p - p random matrix distributed independent of X, according to the Wishart distribution W(n, [Sigma]). For estimating [mu], we consider estimators of the form [delta] = [delta](X, A). We obtain families of Bayes, minimax and admissible minimax estimators with respect to the quadratic loss function ([delta] - [mu])' [Sigma]-1([delta] - [mu]) where [Sigma] is unknown. This paper extends previous results of the author [1], given for the case in which the covariance matrix of the distribution is of the form [sigma]2I, where [sigma] is known.