Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification
Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification
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模型错误指定下三步欧氏似然估计量的大样本特性
DOI：
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发表时间：
2016
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影响因子：
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通讯作者：
P. Dovonon
中科院分区：
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作者：
P. Dovonon
本文研究了Antoine et al.（2007）在全局错定模型中提出的三步欧几里得似然（3S）估计量及其修正版本。我们证明了3S估计量保持-收敛和渐近高斯分布。收缩因子的不连续性使得校正3s估计量的分析难以在错误的模型中进行。我们建议对该因子稍加修改，以控制其在规格错误情况下的发散率。我们证明了所得到的修正3s估计量在规范模型中也是高阶等价于最大经验似然（EL）估计量，在不规范模型中是-收敛和渐近高斯估计量。给出了它的渐近分布对错规范的鲁棒性。由于这些性质，3S和修正3S估计量都可以被认为是Schennach（2007）提出的指数倾斜经验似然估计量的计算吸引力替代品，后者在良好指定的模型中也相当于EL的高阶，在错误指定的模型中也具有-收敛性。
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.