Generalized Neyman-Pearson optimality of empirical likelihood for testing parameter hypotheses

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Abstract

This paper studies the Generalized Neyman-Pearson (GNP) optimality of empirical likelihood-based tests for parameter hypotheses. The GNP optimality focuses on the large deviation errors of tests, i.e., the convergence rates of the type I and II error probabilities under fixed alternatives. We derive (i) the GNP optimality of the empirical likelihood criterion (ELC) test against all alternatives, and (ii) a necessary and a sufficient condition for the GNP optimality of the empirical likelihood ratio (ELR) test against each alternative.

Original languageEnglish
Pages (from-to)773-787
Number of pages15
JournalAnnals of the Institute of Statistical Mathematics
Volume61
Issue number4
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes

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Empirical Likelihood
Optimality
Testing
Alternatives
Type II error
Type I error
Likelihood Ratio Test
Error Probability
Large Deviations
Rate of Convergence
Necessary
Sufficient Conditions

Keywords

  • Empirical likelihood
  • Generalized Neyman-Pearson optimality

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

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AB - This paper studies the Generalized Neyman-Pearson (GNP) optimality of empirical likelihood-based tests for parameter hypotheses. The GNP optimality focuses on the large deviation errors of tests, i.e., the convergence rates of the type I and II error probabilities under fixed alternatives. We derive (i) the GNP optimality of the empirical likelihood criterion (ELC) test against all alternatives, and (ii) a necessary and a sufficient condition for the GNP optimality of the empirical likelihood ratio (ELR) test against each alternative.

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