Explicit estimators under m-dependence for a multivariate normal distribution

Abstract

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.

More on explicit estimators for a banded covariance matrix

“…Some properties of the estimators where given in [12], where it was shown that the estimatorΣ (1) (p) = (σ ij ) given in Proposition 2.1 is consistent. But, the estimator for the covariance matrix above lacks the property of unbiasedness.…”

“…In [12] an explicit estimator for the covariance matrix for a multivariate normal distribution when the covariance matrix have an m-dependence structure is presented. Ohlson et al [12] propose estimators for the general case when m + 1 < p < n and establish some properties of it.…”

“…Ohlson et al [12] propose estimators for the general case when m + 1 < p < n and establish some properties of it. Furthermore, they also consider the special case where m = 1 in detail and in this section some of the results from the article will be presented.…”

“…With huge datasets estimating with iterative methods can be a slow and tedious job. This paper will discuss some properties of an explicit non-iterative estimator for a banded covariance matrix derived in [12] and present an improvement to this estimator. The improvement gives an unbiased and consistent estimator for the mean and the covariance matrix under the special case of first order dependence.…”

“…Section 2 presents the explicit estimator given by [12] and some results regarding it. From these results a new unbiased explicit estimator is suggested.…”