The Annals of Statistics

Necessary and Sufficient Conditions for Explicit Solutions in the Multivariate Normal Estimation Problem for Patterned Means and Covariances

Ted H. Szatrowski

Full-text: Open access

Abstract

The problem of finding maximum likelihood estimates for patterned means and covariance matrices in multivariate analysis is considered. Necessary and sufficient conditions are presented for the existence of explicit solutions and the obtaining of these explicit solutions in one iteration of the scoring equations from any positive definite starting point. Cases in which averaging yields the explicit maximum likelihood estimates are discussed. These results can be applied to the problems of finding maximum likelihood estimates for the parameters in the complete, compound and circular symmetry patterns; mixed models in the analysis of variance; and for finding asymptotic distributions of likelihood ratio statistics when the parameters under the null hypothesis have explicit maximum likelihood estimates.

Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 802-810.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345072

Digital Object Identifier
doi:10.1214/aos/1176345072

Mathematical Reviews number (MathSciNet)
MR572623

Zentralblatt MATH identifier
0497.62045

JSTOR
links.jstor.org

Subjects
Primary: 62H05: Characterization and structure theory
Secondary: 62H15: Hypothesis testing

Keywords
Analysis of variance averaging circular symmetry complete symmetry compound symmetry convergence explicit solutions maximum likelihood estimation mixed model patterned covariance matrices patterned means

Citation

Szatrowski, Ted H. Necessary and Sufficient Conditions for Explicit Solutions in the Multivariate Normal Estimation Problem for Patterned Means and Covariances. Ann. Statist. 8 (1980), no. 4, 802--810. doi:10.1214/aos/1176345072. https://projecteuclid.org/euclid.aos/1176345072


Export citation