Toma Aida
Department of Applied Mathematics, Bucharest University of Economic Studies, 010374 Bucharest, Romania.
"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania.
Entropy (Basel). 2023 Jun 30;25(7):1013. doi: 10.3390/e25071013.
In the present paper, we introduce a class of robust Z-estimators for moment condition models. These new estimators can be seen as robust alternatives for the minimum empirical divergence estimators. By using the multidimensional Huber function, we first define robust estimators of the element that realizes the supremum in the dual form of the divergence. A linear relationship between the influence function of a minimum empirical divergence estimator and the influence function of the estimator of the element that realizes the supremum in the dual form of the divergence led to the idea of defining new Z-estimators for the parameter of the model, by using robust estimators in the dual form of the divergence. The asymptotic properties of the proposed estimators were proven, including here the consistency and their asymptotic normality. Then, the influence functions of the estimators were derived, and their robustness is demonstrated.
在本文中，我们介绍了一类用于矩条件模型的稳健Z估计量。这些新的估计量可被视为最小经验散度估计量的稳健替代方法。通过使用多维休伯函数，我们首先定义了在散度对偶形式中实现上确界的元素的稳健估计量。最小经验散度估计量的影响函数与在散度对偶形式中实现上确界的元素的估计量的影响函数之间的线性关系，引出了通过在散度对偶形式中使用稳健估计量来为模型参数定义新的Z估计量的想法。我们证明了所提出估计量的渐近性质，包括一致性和渐近正态性。然后，推导了估计量的影响函数，并证明了它们的稳健性。
