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Robust Estimation with Exponentially Tilted Hellinger Distance

Author

Listed:
  • Bertille Antoine

    (Simon Fraser University)

  • Prosper Dovonon

    (Concordia University)

Abstract
This paper is concerned with estimation of parameters defined by moment equalities. We introduce the exponentially tilted Hellinger distance (ETHD) estimator which is efficient under correct specification, and robust to both global and local misspecification. In the spirit of Schennach (2007), ETHD combines the Hellinger distance and the Kullback-Leibler information criterion. We show that it achieves optimal minimax robust properties under local deviations from the model and remains well-behaved under global misspecification.

Suggested Citation

  • Bertille Antoine & Prosper Dovonon, 2020. "Robust Estimation with Exponentially Tilted Hellinger Distance," Discussion Papers dp20-02, Department of Economics, Simon Fraser University.
    • Handle: RePEc:sfu:sfudps:dp20-02
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    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, January.
    3. Aviv Nevo & Adam M. Rosen, 2012. "Identification With Imperfect Instruments," The Review of Economics and Statistics, MIT Press, vol. 94(3), pages 659-671, August.
    4. Hall, Alastair R. & Inoue, Atsushi, 2003. "The large sample behaviour of the generalized method of moments estimator in misspecified models," Journal of Econometrics, Elsevier, vol. 114(2), pages 361-394, June.
    5. Maasoumi, Esfandiar & Phillips, Peter C. B., 1982. "On the behavior of inconsistent instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 183-201, August.
    6. Richard Ashley, 2009. "Assessing the credibility of instrumental variables inference with imperfect instruments via sensitivity analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 325-337, March.
    7. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, September.
    8. Nikolay Gospodinov & Raymond Kan & Cesare Robotti, 2014. "Misspecification-Robust Inference in Linear Asset-Pricing Models with Irrelevant Risk Factors," The Review of Financial Studies, Society for Financial Studies, vol. 27(7), pages 2139-2170.
    9. Patrik Guggenberger, 2008. "Finite Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 526-541.
    10. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, September.
    11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    12. Almeida, Caio & Garcia, René, 2012. "Assessing misspecified asset pricing models with empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 170(2), pages 519-537.
    13. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    14. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    15. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    16. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, September.
    17. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, September.
    18. Nikolay Gospodinov & Esfandiar Maasoumi, 2017. "General Aggregation of Misspecified Asset Pricing Models," FRB Atlanta Working Paper 2017-10, Federal Reserve Bank of Atlanta.
    19. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    20. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    21. Caio Almeida & René Garcia, 2017. "Economic Implications of Nonlinear Pricing Kernels," Management Science, INFORMS, vol. 63(10), pages 3361-3380, October.
    22. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    23. Raymond Kan & Cesare Robotti & Jay Shanken, 2013. "Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology," Journal of Finance, American Finance Association, vol. 68(6), pages 2617-2649, December.
    24. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, September.
    25. Maasoumi, Esfandiar, 1990. "How to live with misspecification if you must," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 67-86.
    26. Timothy G. Conley & Christian B. Hansen & Peter E. Rossi, 2012. "Plausibly Exogenous," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 260-272, February.
    27. Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(2), pages 387-421, April.
    28. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    29. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, September.
    30. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, May.
    31. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    32. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    33. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

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    3. Gospodinov, Nikolay & Maasoumi, Esfandiar, 2021. "Generalized aggregation of misspecified models: With an application to asset pricing," Journal of Econometrics, Elsevier, vol. 222(1), pages 451-467.

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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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