Explicit estimators under <Emphasis Type="Italic">m</Emphasis>-dependence for a multivariate normal distribution

The problem of estimating parameters of a multivariate normal p-dimensional random vector is considered for a banded covariance structure reflecting m-dependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m.