ROBUST ESTIMATION WITH EXPONENTIALLY TILTED HELLINGER DISTANCE

Bertille Antoine and Prosper Dovonon ()
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Prosper Dovonon: Concordia University, https://sites.google.com/site/prosperdovonon/

Discussion Papers from Department of Economics, Simon Fraser University

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 spec- ified 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 spec- ification 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.

Keywords: moment condition models; global misspecification; local misspecification; Hellinger dis- tance; minimax robust estimation; semiparametric efficiency. (search for similar items in EconPapers)
Date: 2018-11
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Related works:
Journal Article: Robust estimation with exponentially tilted Hellinger distance (2021)
Working Paper: Robust Estimation with Exponentially Tilted Hellinger Distance (2020)
Working Paper: Robust Estimation with Exponentially Tilted Hellinger Distance (2018)
Working Paper: ROBUST ESTIMATION WITH EXPONENTIALLY TILTED HELLINGER DISTANCE (2017)
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