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Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification

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  • Prosper Dovonon

Abstract

This article studies the three-step Euclidean likelihood (3S) estimator and its corrected version as proposed by Antoine et al. (2007) in globally misspecified models. We establish that the 3S estimator stays -convergent and asymptotically Gaussian. The discontinuity in the shrinkage factor makes the analysis of the corrected-3S estimator harder to carry out in misspecified models. We propose a slight modification to this factor to control its rate of divergence in case of misspecification. We show that the resulting modified-3S estimator is also higher order equivalent to the maximum empirical likelihood (EL) estimator in well-specified models and -convergent and asymptotically Gaussian in misspecified models. Its asymptotic distribution robust to misspecification is also provided. Because of these properties, both the 3S and the modified-3S estimators could be considered as computationally attractive alternatives to the exponentially tilted empirical likelihood estimator proposed by Schennach (2007) which also is higher order equivalent to EL in well-specified models and -convergent in misspecified models.

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  • 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.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:4:p:465-514
    DOI: 10.1080/07474938.2014.966634
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