More on explicit estimators for a banded covariance matrix
The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and an unbiased estimator can be proposed. A new and easier proof of consistency is then presented.
This theory is also generalized to a general linear model where the corresponding theorems and propositions are stated to establish unbiasedness and consistency.