The problem of estimating mean and covariances of a multivariate normal distributedrandom vector has been studied in many forms. This thesis focuses on the estimatorsproposed in [15] for a banded covariance structure with m-dependence. It presents theprevious results of the estimator and rewrites the estimator when m = 1, thus makingit easier to analyze. This leads to an adjustment, and a proposition for an unbiasedestimator can be presented. A new and easier proof of consistency is then presented.This theory is later generalized into a general linear model where the correspondingtheorems and propositions are made to establish unbiasedness and consistency. In thelast chapter some simulations with the previous and new estimator verifies that thetheoretical results indeed makes an impact.