Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification
研究了三步欧几里得似然估计量在全局误设定模型下的性质，证明其根号n收敛且渐近正态，并提出了修正版本，为计算上更简便的替代方案提供了理论依据。
This article studies the three-step Euclidean likelihood (3S) estimator and its corrected version as proposed by Antoine et al. (2007 Antoine, B., Bonnal, H., Renault, E. (2007). On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood. Journal of Econometrics 138:461–487.[Crossref], [Web of Science ®] , [Google Scholar]) 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 Schennach, S. M. (2007). Point estimation with exponentially tilted empirical likelihood. Annals of Statistics 35:634–672.[Crossref], [Web of Science ®] , [Google Scholar]) which also is higher order equivalent to EL in well-specified models and -convergent in misspecified models.