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December, 1989 Stochastic Inequalities Relating a Class of Log-Likelihood Ratio Statistics to their Asymptotic $\chi^2$ Distribution
B. T. Porteous
Ann. Statist. 17(4): 1723-1734 (December, 1989). DOI: 10.1214/aos/1176347390

Abstract

For decomposable covariance selection models, stochastic inequalities which relate the null distribution of the log-likelihood ratio statistic to its asymptotic $\chi^2$ distribution are obtained. The implications are twofold: First, the null distribution of the log-likelihood ratio statistic is seen to be stochastically larger than its asymptotic $\chi^2$ distribution. Extremely large samples apart, for the $\chi^2$ approximation to be valid, a deflation of the log-likelihood ratio statistic is then necessary. Second, a simple adjustment to the log-likelihood ratio statistic, similar in spirit to the Bartlett adjustment, yields a conservative test.

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B. T. Porteous. "Stochastic Inequalities Relating a Class of Log-Likelihood Ratio Statistics to their Asymptotic $\chi^2$ Distribution." Ann. Statist. 17 (4) 1723 - 1734, December, 1989. https://doi.org/10.1214/aos/1176347390

Information

Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0694.62010
MathSciNet: MR1026308
Digital Object Identifier: 10.1214/aos/1176347390

Subjects:
Primary: 62E15
Secondary: 62H99

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 4 • December, 1989
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