Note on Estimating the Eigen System of Σ1-1Σ2

Title & Authors
Note on Estimating the Eigen System of Σ1-1Σ2
Kim, Myung-Geun;

Abstract
The maximum likelihood estimators of the eigenvalues and eigenvectors of \$$\small{\Sigma}$$\small{_1}$^{-1}\$$\small{\Sigma}$$\small{_2}$are shown to be the eigenvalues and eigenvectors of \$S$\small{_1}$^{1}\$S$\small{_2}$ under multivariate normality and are explicitly derived. The nature of the eigenvalues and eigenvectors of \$$\small{\Sigma}$$\small{_1}$^{-1}\$$\small{\Sigma}$$\small{_2}$ or their estimators will be uncovered.
Keywords
Eigenvalue;eigenvector;maximum likelihood estimator;
Language
English
Cited by
References
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Aspects of Multivariate Statistical Theory, 1982.

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Multivariate Analysis VI, 1985. pp.431-447

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Annals of Statistics, 1973. vol.1. pp.763-765