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Robust Estimation with Exponentially Tilted Hellinger Distance

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  • Bertille Antoine
  • Prosper Dovonon

Abstract

This paper is concerned with estimation of parameters defined by moment equalities. In this context, Kitamura, Otsu and Evdokimov (2013a) have introduced the minimum Hellinger distance (HD) estimator which is asymptotically semiparametrically efficient when the model is correctly specified and achieves optimal minimax robust properties under small deviations from the model (local misspecification). This paper evaluates the performance of inference procedures under two comple-mentary types of misspecification, local and global. After showing that HD is not robust to global misspecification, we introduce, in the spirit of Schennach (2007), the exponentially tilted Hellinger distance (ETHD) estimator by combining the Hellinger distance and the Kullback-Leibler information criterion. Our estimator shares the same desirable asymptotic properties as HD under correct specification and local misspecification, and remains well-behaved under global misspecification. ETHD therefore appears to be the first estimator that is efficient under correct specification, and robust to both global and local misspecification.

Suggested Citation

  • Bertille Antoine & Prosper Dovonon, 2018. "Robust Estimation with Exponentially Tilted Hellinger Distance," CIRANO Working Papers 2018s-38, CIRANO.
    • Handle: RePEc:cir:cirwor:2018s-38
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    File URL: https://cirano.qc.ca/files/publications/2018s-38.pdf
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    More about this item

    Keywords

    Moment Condition Models; Global Misspecification; Local Misspecification; Hellinger Distance; Minimax Robust Estimation; Semiparametric Efficiency;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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