Moderate deviations of generalized method of moments and empirical likelihood estimators

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Abstract

This paper studies moderate deviation behaviors of the generalized method of moments and generalized empirical likelihood estimators for generalized estimating equations, where the number of equations can be larger than the number of unknown parameters. We consider two cases for the data generating probability measure: the model assumption and local contaminations or deviations from the model assumption. For both cases, we characterize the first-order terms of the moderate deviation error probabilities of these estimators. Our moderate deviation analysis complements the existing literature of the local asymptotic analysis and misspecification analysis for estimating equations, and is useful to evaluate power and robust properties of statistical tests for estimating equations which typically involve some estimators for nuisance parameters.

Original languageEnglish
Pages (from-to)1203-1216
Number of pages14
JournalJournal of Multivariate Analysis
Volume102
Issue number8
DOIs
Publication statusPublished - 2011 Sep 1
Externally publishedYes

Keywords

  • 60F10
  • 62F12
  • Empirical likelihood
  • Estimating equation
  • Moderate deviation

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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