摘要翻译：
线性回归模型广泛应用于经济学、统计学和许多其他学科的实证工作中。研究人员经常在线性模型规范中包含许多协变量，试图控制混杂因素。我们给出了允许许多协变量和异方差的推理方法。我们的结果是使用高维近似得到的，其中包含的协变量的数量允许随着样本量的增长而增长。我们发现线性模型的Eicker-White异方差一致性标准误差估计在这种渐近性下都是不一致的。然后，我们提出了一个新的异方差一致性标准误差公式，该公式对未知形式的（条件）异方差和可能包含许多协变量都是完全自动和鲁棒的。我们将我们的发现应用于三个设置：多协变量的参数线性模型、多固定效应的线性面板模型和多技术回归的半参数半线性模型。文中还提供了与理论结果相一致的模拟证据。文中还通过一个实际应用对所提出的方法进行了说明。
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英文标题：
《Inference in Linear Regression Models with Many Covariates and
  Heteroskedasticity》
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作者：
Matias D. Cattaneo, Michael Jansson, Whitney K. Newey
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最新提交年份：
2017
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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：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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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：
  The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroskedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates are allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroskedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroskedasticity consistent standard error formula that is fully automatic and robust to both (conditional)\ heteroskedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is also provided. The proposed methods are also illustrated with an empirical application.
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PDF链接：
https://arxiv.org/pdf/1507.02493