Jenish Nazgul, Prucha Ingmar R
Department of Economics, New York University, 19 West 4th Street, New York, NY 10012. Tel.: 212-998-3891.
J Econom. 2012 Sep;170(1):178-190. doi: 10.1016/j.jeconom.2012.05.022.
The development of a general inferential theory for nonlinear models with cross-sectionally or spatially dependent data has been hampered by a lack of appropriate limit theorems. To facilitate a general asymptotic inference theory relevant to economic applications, this paper first extends the notion of near-epoch dependent (NED) processes used in the time series literature to random fields. The class of processes that is NED on, say, an α-mixing process, is shown to be closed under infinite transformations, and thus accommodates models with spatial dynamics. This would generally not be the case for the smaller class of α-mixing processes. The paper then derives a central limit theorem and law of large numbers for NED random fields. These limit theorems allow for fairly general forms of heterogeneity including asymptotically unbounded moments, and accommodate arrays of random fields on unevenly spaced lattices. The limit theorems are employed to establish consistency and asymptotic normality of GMM estimators. These results provide a basis for inference in a wide range of models with spatial dependence.
由于缺乏合适的极限定理，针对具有横截面或空间依赖性数据的非线性模型构建一般推断理论的进展一直受阻。为了推动与经济应用相关的一般渐近推断理论的发展，本文首先将时间序列文献中使用的近 epoch 相依（NED）过程的概念扩展到随机场。例如，在一个α - 混合过程上是 NED 的过程类，在无限变换下是封闭的，因此适用于具有空间动态的模型。对于较小的α - 混合过程类，情况通常并非如此。然后，本文推导了 NED 随机场的中心极限定理和大数定律。这些极限定理允许相当一般形式的异质性，包括渐近无界矩，并适用于在不均匀间隔格点上的随机场阵列。利用这些极限定理建立了广义矩估计量（GMM）的一致性和渐近正态性。这些结果为在广泛的具有空间依赖性的模型中进行推断提供了基础。
