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Point estimation with exponentially tilted empirical likelihood

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  • Susanne M. Schennach

Abstract

Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its $O(n^{-1})$ bias is small and that bias-corrected EL is higher-order efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that, in the presence of model misspecification, EL may cease to be root n convergent when the functions defining the moment conditions are unbounded (even when their expectations are bounded). In contrast, the related exponential tilting (ET) estimator avoids this problem. This paper shows that the ET and EL estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood (ETEL) exhibiting the same $O(n^{-1})$ bias and the same $O(n^{-2})$ variance as EL, while maintaining root n convergence under model misspecification.

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File URL: http://arxiv.org/pdf/0708.1874
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Paper provided by arXiv.org in its series Papers with number 0708.1874.

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Date of creation: Aug 2007
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Publication status: Published in Annals of Statistics 2007, Vol. 35, No. 2, 634-672
Handle: RePEc:arx:papers:0708.1874

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  1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, Econometric Society, vol. 72(1), pages 219-255, 01.
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Cited by:
  1. Pierre Chaussé, . "Computing Generalized Method of Moments and Generalized Empirical Likelihood with R," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 34(i11).
  2. Alain Guay & Jean-François Lamarche, 2008. "The Information Content of Implied Probabilities to Detect Structural Change," Cahiers de recherche 0833, CIRPEE.
  3. Israelov, Roni & Lugauer, Steven, 2011. "Combining empirical likelihood and generalized method of moments estimators: Asymptotics and higher order bias," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1339-1347, September.
  4. Camponovo, Lorenzo & Otsu, Taisuke, 2014. "On Bartlett correctability of empirical likelihood in generalized power divergence family," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 38-43.
  5. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.
  6. Taisuke Otsu & Myung Hwan Seo & Yoon-Jae Whang, 2008. "Testing for Non-Nested Conditional Moment Restrictions Using Unconditional Empirical Likelihood," Cowles Foundation Discussion Papers 1660, Cowles Foundation for Research in Economics, Yale University.
  7. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
  8. Lô, Serigne N. & Ronchetti, Elvezio, 2012. "Robust small sample accurate inference in moment condition models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3182-3197.
  9. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
  10. Sueishi, Naoya, 2013. "Identification problem of the exponential tilting estimator under misspecification," Economics Letters, Elsevier, vol. 118(3), pages 509-511.
  11. Canay, Ivan A. & Otsu, Taisuke, 2012. "Hodges–Lehmann optimality for testing moment conditions," Journal of Econometrics, Elsevier, vol. 171(1), pages 45-53.
  12. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
  13. Seojeong Lee, 2014. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for GEL Estimators," Discussion Papers, School of Economics, The University of New South Wales 2014-02, School of Economics, The University of New South Wales.
  14. Sanjay Chaudhuri & Malay Ghosh, 2011. "Empirical likelihood for small area estimation," Biometrika, Biometrika Trust, Biometrika Trust, vol. 98(2), pages 473-480.
  15. Sowell, Fallaw, 2009. "The empirical saddlepoint likelihood estimator applied to two-step GMM," MPRA Paper 15494, University Library of Munich, Germany, revised May 2009.
  16. Pierre Chaussé, 2011. "Generalized empirical likelihood for a continuum of moment conditions," Working Papers 1104, University of Waterloo, Department of Economics, revised Oct 2011.
  17. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2009. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Cowles Foundation Discussion Papers 1720, Cowles Foundation for Research in Economics, Yale University.
  18. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.

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