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Hodges–Lehmann optimality for testing moment conditions

  • Canay, Ivan A.
  • Otsu, Taisuke

This paper studies the Hodges and Lehmann (1956) optimality of tests in a general setup. The tests are compared by the exponential rates of growth to one of the power functions evaluated at a fixed alternative while keeping the asymptotic sizes bounded by some constant. We present two sets of sufficient conditions for a test to be Hodges–Lehmann optimal. These new conditions extend the scope of the Hodges–Lehmann optimality analysis to setups that cannot be covered by other conditions in the literature. The general result is illustrated by our applications of interest: testing for moment conditions and overidentifying restrictions. In particular, we show that (i) the empirical likelihood test does not necessarily satisfy existing conditions for optimality but does satisfy our new conditions; and (ii) the generalized method of moments (GMM) test and the generalized empirical likelihood (GEL) tests are Hodges–Lehmann optimal under mild primitive conditions. These results support the belief that the Hodges–Lehmann optimality is a weak asymptotic requirement.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 171 (2012)
Issue (Month): 1 ()
Pages: 45-53

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Handle: RePEc:eee:econom:v:171:y:2012:i:1:p:45-53
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, 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. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  5. Yuichi Kitamura & Andres Santos & Azeem M. Shaikh, 2012. "On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 80(1), pages 413-423, 01.
  6. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  7. Nelson, Forrest D & Savin, N E, 1990. "The Danger of Extrapolating Asymptotic Local Power," Econometrica, Econometric Society, vol. 58(4), pages 977-81, July.
  8. Otsu, Taisuke, 2010. "On Bahadur efficiency of empirical likelihood," Journal of Econometrics, Elsevier, vol. 157(2), pages 248-256, August.
  9. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
  10. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  11. Kallenberg, Wilbert C. M. & Kourouklis, Stavros, 1992. "Hodges-Lehmann optimality of tests," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 31-38, May.
  12. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
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