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December, 1984 An Asymptotic Expansion of the Nonnull Distribution of Wilks Criterion for Testing the Multivariate Linear Hypothesis
R. W. Kulp, B. N. Nagarsenker
Ann. Statist. 12(4): 1576-1583 (December, 1984). DOI: 10.1214/aos/1176346816

Abstract

An asymptotic expansion of the nonnull distribution of the Wilks statistic for testing the linear hypothesis in multivariate analysis of variance is obtained up to the order $N^{-2}$ where $N$ is the sample size, for the first time in terms of noncentral beta distributions. The asymptotic distributions are better than the ones available in Anderson (1958) in the null case and in Sugiura and Fujikoshi (1969) and Posten and Bergman (1964) in the nonnull case. In fact, for certain parameters the asymptotic expansion reduces to the first term and we get the exact distribution.

Citation

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R. W. Kulp. B. N. Nagarsenker. "An Asymptotic Expansion of the Nonnull Distribution of Wilks Criterion for Testing the Multivariate Linear Hypothesis." Ann. Statist. 12 (4) 1576 - 1583, December, 1984. https://doi.org/10.1214/aos/1176346816

Information

Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0554.62016
MathSciNet: MR760712
Digital Object Identifier: 10.1214/aos/1176346816

Subjects:
Primary: 62H10
Secondary: 62E20 , 62H15

Keywords: asymptotic expansions , Likelihood ratio criterion , noncentral beta distributions , null and nonnull distributions

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • December, 1984
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