Efficient M-estimators with auxiliary information

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Abstract

This paper introduces a new class of M-estimators based on generalised empirical likelihood (GEL) estimation with some auxiliary information available in the sample. The resulting class of estimators is efficient in the sense that it achieves the same asymptotic lower bound as that of the efficient generalised method of moment (GMM) estimator with the same auxiliary information. The paper also shows that in case of smooth estimating equations the proposed estimators enjoy a small second order bias property compared to both efficient GMM and full GEL estimators. Analytical formulae to obtain bias corrected estimators are also provided. Simulations show that with correctly specified auxiliary information the proposed estimators and in particular those based on empirical likelihood outperform standard M and efficient GMM estimators both in terms of finite sample bias and efficiency. On the other hand with moderately misspecified auxiliary information estimators based on the nonparametric tilting method are typically characterised by the best finite sample properties. (C) 2010 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)3326-3342
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume140
Issue number11
DOIs
Publication statusPublished - Nov 2010

Keywords

  • Asymptotic efficiency
  • Generalised empirical likelihood
  • Generalised method of moments
  • Second order bias
  • EMPIRICAL LIKELIHOOD
  • MOMENT RESTRICTIONS
  • MODELS
  • REGRESSION
  • QUANTILE

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