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June, 1987 Proportionality of Covariance Matrices
P. Svante Eriksen
Ann. Statist. 15(2): 732-748 (June, 1987). DOI: 10.1214/aos/1176350372


The present paper considers inference for the statistical model specifying proportionality between independent Wishart distributions. It is shown that the maximum likelihood estimate of the common covariance matrix and the constants of proportionality is the unique solution to the likelihood equation and an iterative procedure determining the estimator is given. The model is an exponential transformation model, which implies the existence of an exact ancillary (a maximal invariant), and an asymptotic expansion for the distribution of the estimator conditionally on the ancillary is given. In addition, it is shown that the estimator is unbiased to order $O(n^{-3/2})$. Finally, we derive the Bartlett adjustment to the likelihood ratio statistic for the hypothesis of proportionality and subsequently for the hypothesis specifying that all of the constants of proportionality are equal to one. A small simulation study shows that the Bartlett adjustment can be very effective in improving the accuracy of chi-squared approximations.


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P. Svante Eriksen. "Proportionality of Covariance Matrices." Ann. Statist. 15 (2) 732 - 748, June, 1987.


Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0628.62060
MathSciNet: MR888437
Digital Object Identifier: 10.1214/aos/1176350372

Primary: 62H15
Secondary: 62H12, 62J10

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 2 • June, 1987
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