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November, 1977 The Performance of the Likelihood Ratio Test When the Model is Incorrect
Robert V. Foutz, R. C. Srivastava
Ann. Statist. 5(6): 1183-1194 (November, 1977). DOI: 10.1214/aos/1176344003


Let the random variable $X$ have a distribution depending on a parameter $\theta \in \Theta$. Consider the problem of testing the hypothesis $H: \Theta_0 \subseteqq \Theta$ based on a sequence of observations on $X$. The likelihood ratio test for $H$ is constructed by selecting a model for the unknown distribution of $X$. In this paper the asymptotic performance of the likelihood ratio test is studied when the model is incorrect, that is, when the probability distribution of $X$ is not a member of the model from which the likelihood ratio test is constructed. Exact and approximate measures of the asymptotic efficiency of the likelihood ratio test when the model is incorrect are proposed.


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Robert V. Foutz. R. C. Srivastava. "The Performance of the Likelihood Ratio Test When the Model is Incorrect." Ann. Statist. 5 (6) 1183 - 1194, November, 1977.


Published: November, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0391.62004
MathSciNet: MR448684
Digital Object Identifier: 10.1214/aos/1176344003

Primary: 62A10
Secondary: 62F05 , 62F20

Keywords: approximate slope , asymptotic distribution , Bahadur efficiency , exact slope , likelihood ratio , model is incorrect

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • November, 1977
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