High-dimensional econometrics and regularized GMM
High-dimensional econometrics and regularized GMM
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DOI：
10.1920/wp.cem.2018.3518
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发表时间：
2018-06
期刊：
影响因子：
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通讯作者：
A. Belloni;V. Chernozhukov;D. Chetverikov;Christian Hansen;Kengo Kato
中科院分区：
文献类型：
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作者：
A. Belloni;V. Chernozhukov;D. Chetverikov;Christian Hansen;Kengo Kato
本章介绍了高维模型中分析估计和推理的关键概念和理论结果。高维模型的特征是具有许多未知参数，这些参数相对于样本大小并不是零的。我们首先在一个框架中给出结果，其中感兴趣的参数的估计器可以直接表示为近似平均。在此背景下，我们回顾了一些基本结果，包括高维中心极限定理、高维极限分布的Bootstrap逼近和中等偏差理论。我们还回顾了当许多参数感兴趣时进行推理的关键概念，例如具有家族错误率或错误发现率控制的多重测试。然后，我们转向一般的高维最小距离框架，特别关注广义矩方法问题，其中我们给出了关于模型参数的估计和推断的结果。目前的结果涵盖了广泛的计量经济学应用，我们讨论了几个主要的特殊情况，包括高维线性回归和线性工具变量模型，以说明一般结果。
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small relative to the sample size. We first present results in a framework where estimators of parameters of interest may be represented directly as approximate means. Within this context, we review fundamental results including high-dimensional central limit theorems, bootstrap approximation of high-dimensional limit distributions, and moderate deviation theory. We also review key concepts underlying inference when many parameters are of interest such as multiple testing with family-wise error rate or false discovery rate control. We then turn to a general high-dimensional minimum distance framework with a special focus on generalized method of moments problems where we present results for estimation and inference about model parameters. The presented results cover a wide array of econometric applications, and we discuss several leading special cases including high-dimensional linear regression and linear instrumental variables models to illustrate the general results.