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January, 1974 Asymptotic Expansions of the Non-Null Distributions of Likelihood Ratio Criteria for Covariance Matrices
C. G. Khatri, M. S. Srivastava
Ann. Statist. 2(1): 109-117 (January, 1974). DOI: 10.1214/aos/1176342617

Abstract

In this paper, asymptotic expansions of the non-null distributions of the likelihood ratio criteria are obtained for testing the hypotheses: (a) $H_1: \Sigma = \sigma^2I, \sigma^2 > 0$, (b) $H_2: \Sigma_1 = \Sigma_2$, against alternatives which are close to the hypothesis. These expansions are of chi-square type. The first problem has been considered by Sugiura (1969) but because of the singularity at the hypothesis, his expansion will not be good for alternatives close to the hypothesis. The second problem has been considered by de Waal (1970) but the expansion given by him is invalid.

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C. G. Khatri. M. S. Srivastava. "Asymptotic Expansions of the Non-Null Distributions of Likelihood Ratio Criteria for Covariance Matrices." Ann. Statist. 2 (1) 109 - 117, January, 1974. https://doi.org/10.1214/aos/1176342617

Information

Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0296.62037
MathSciNet: MR345317
Digital Object Identifier: 10.1214/aos/1176342617

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

Keywords: Asymptotic non-null distributions , chi-square distribution , equality of covariances , likelihood ratio tests , sphericity

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • January, 1974
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