Maximum likelihood estimation for multivariate normal samples : theory and methods

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Authors

Strydom, Hendrina Fredrika
Crowther, N.A.S. (Nicolaas Andries Sadie), 1944-

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South African Statistical Association

Abstract

Maximum likelihood estimation of parameter structures in the case of multivariate normal samples is considered. The procedure provides a new statistical methodology for maximum likelihood estimation which does not require derivation and solution of the likelihood equations. It is a flexible procedure for the analysis of specific structures in mean vectors and covariance matrices – including the case where the sample size is small relative to the dimension of the observations. Special cases include different variations of the Behrens-Fisher problem, proportional covariancematrices and proportional mean vectors. Specific structures are illustrated with real data examples.

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Keywords

Behrens-Fisher, Canonical statistic, Maximum likelihood (ML) estimation, Multivariate normal samples, Parameter structures, Proportional covariance matrices, Toeplitz correlation structure

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Citation

Strydom, HF & Crowther, NAS 2012, 'Maximum likelihood estimation for multivariate normal samples : theory and methods', South African Statistical Journal, vol. 46, no. 1, pp. 115-153.