摘要翻译：
本章介绍了分析高维模型中的估计和推断的关键概念和理论结果。高维模型的特点是具有许多未知参数，这些参数相对于样本量并不是完全小。我们首先在一个框架中给出了结果，其中感兴趣参数的估计量可以直接表示为近似平均。在此背景下，我们回顾一些基本结果，包括高维中心极限定理，高维极限分布的bootstrap逼近，以及中等偏差理论。我们还回顾了当许多参数是感兴趣的，如多重测试与家庭错误率或错误发现率控制时，推理的关键概念。然后我们转向一个一般的高维最小距离框架，特别关注广义矩量法问题，在那里我们给出了关于模型参数的估计和推断的结果。所给出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来说明一般结果。
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英文标题：
《High-Dimensional Econometrics and Regularized GMM》
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作者：
Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, Christian
  Hansen, and Kengo Kato
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最新提交年份：
2018
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/1806.01888