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Robustness, Infinitesimal Neighborhoods, and Moment Restrictions

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Abstract

This paper is concerned with robust estimation under moment restrictions. A moment restriction model is semiparametric and distribution-free, therefore it imposes mild assumptions. Yet it is reasonable to expect that the probability law of observations may have some deviations from the ideal distribution being modeled, due to various factors such as measurement errors. It is then sensible to seek an estimation procedure that are robust against slight perturbation in the probability measure that generates observations. This paper considers local deviations within shrinking topological neighborhoods to develop its large sample theory, so that both bias and variance matter asymptotically. The main result shows that there exists a computationally convenient estimator that achieves optimal minimax robust properties. It is semiparametrically efficient when the model assumption holds, and at the same time it enjoys desirable robust properties when it does not.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1720.

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Length: 39 pages
Date of creation: Aug 2009
Date of revision:
Publication status: Published in Econometrica (May 2013) 81(3): 1185-1201
Handle: RePEc:cwl:cwldpp:1720

Note: CFP 1382
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Keywords: Asymptotic minimax theorem; Hellinger distance; Semiparametric efficiency;

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  1. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
  2. 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.
  3. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," Harvard Institute of Economic Research Working Papers 1736, Harvard - Institute of Economic Research.
  4. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 891-916, July.
  5. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, Econometric Society, vol. 65(4), pages 861-874, July.
  6. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," Levine's Bibliography 321307000000000307, UCLA Department of Economics.
  7. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," Cowles Foundation Discussion Papers 1569, Cowles Foundation for Research in Economics, Yale University.
  10. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1661-1672, November.
  11. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 107(441), pages 503-19, March.
  12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
  13. repec:cup:cbooks:9780521496032 is not listed on IDEAS
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Cited by:
  1. 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.
  2. Lorenzo Camponovo & Taisuke Otsu, 2011. "Robustness of Bootstrap in Instrumental Variable Regression," Cowles Foundation Discussion Papers 1796, Cowles Foundation for Research in Economics, Yale University.

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