The Annals of Mathematical Statistics

Matrix Methods in Components of Variance and Covariance Analysis

S. R. Searle

Full-text: Open access

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.

Article information

Source
Ann. Math. Statist. Volume 27, Number 3 (1956), 737-748.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728180

Digital Object Identifier
doi:10.1214/aoms/1177728180

Mathematical Reviews number (MathSciNet)
MR81051

Zentralblatt MATH identifier
0074.14207

JSTOR
links.jstor.org

Citation

Searle, S. R. Matrix Methods in Components of Variance and Covariance Analysis. Ann. Math. Statist. 27 (1956), no. 3, 737--748. doi:10.1214/aoms/1177728180. https://projecteuclid.org/euclid.aoms/1177728180


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