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January, 1978 Large Deviations of Likelihood Ratio Statistics with Applications to Sequential Testing
Michael Woodroofe
Ann. Statist. 6(1): 72-84 (January, 1978). DOI: 10.1214/aos/1176344066

Abstract

We study the tail of the null distribution of the $\log$ likelihood ratio statistic for testing sharp hypotheses about the parameters of an exponential family. We show that the classical chisquare approximation is of exactly the right order of magnitude, although it may be off by a constant factor. We then apply our results and techniques to find the error probabilities of a sequential version of the likelihood ratio test. The sequential version rejects if the likelihood ratio statistic crosses a given barrier by a given time. Our approach uses a local limit theorem which takes account of large deviations and integrates the local result by using the theory of Hausdorff measures.

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Michael Woodroofe. "Large Deviations of Likelihood Ratio Statistics with Applications to Sequential Testing." Ann. Statist. 6 (1) 72 - 84, January, 1978. https://doi.org/10.1214/aos/1176344066

Information

Published: January, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0386.62019
MathSciNet: MR455183
Digital Object Identifier: 10.1214/aos/1176344066

Subjects:
Primary: 62E20
Secondary: 62G10

Keywords: conditional probabilities , exponential families , Hausdorff measures , large deviations , Local limit theorems , sequential tests

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 1 • January, 1978
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