Matrix Methods in Components of Variance and Covariance Analysis

Abstract

The sampling variance of the least squares estimates of the components of variance in an unbalanced (non-orthogonal) one-way classification and the large sample variances of the maximum likelihood estimates of these quantities are summarized in a paper by Crump [1]. The present paper outlines a method of obtaining these results by the use of matrix algebra, and extends them to the sampling variances of estimates of components of covariance when two variables are considered. The methods are also used to obtain the large sample variance-covariance matrix of the maximum likelihood estimates of the components of variance and covariance.