Mean estimation for a partitioned multinormal distribution

Let X be a p 0-normal random vector with unknown μ and known variance-covariance matrix Σ and let X be partitioned as X = (X′(1),X′(2))′ where X (j) is a subvector of X with dimension p j such that . Some optimum properties of the maximum likelihood estimator (m.l.e.) of μ, the mean vector, are given. This estimator is computed on the basis of a sample drawn from the whole vector X of dimension p 0 and two additional samples drawn from X (1) X (2) respectively. All three samples are assumed to be independent. This estimator is also compared with the usual estimator X which is based solely on the sample from the entire vector X and hence ignores the extra information provided by the other two samples.