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High-Dimensional Econometrics and Regularized GMM

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  • Alexandre Belloni
  • Victor Chernozhukov
  • Denis Chetverikov
  • Christian Hansen
  • Kengo Kato

Abstract

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.

Suggested Citation

  • Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-Dimensional Econometrics and Regularized GMM," Papers 1806.01888, arXiv.org, revised Jun 2018.
  • Handle: RePEc:arx:papers:1806.01888
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    Cited by:

    1. Baris Ata & Alexandre Belloni & Ozan Candogan, 2018. "Latent Agents in Networks: Estimation and Pricing," Papers 1808.04878, arXiv.org, revised Dec 2018.

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