High-dimensional econometrics and regularized GMM
By Alexandre Belloni, Victor Chernozhukov, D. Chetverikov, Christian Hansen, Kengo Kato. 2018
72 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistics and Probability
- Victor Chernozhukov
- D. Chetverikov
- Yuta Koike
- Kengo Kato
- Alexandre Belloni
- Christian Hansen
- Whitney K. Newey
- Stefan Wager
Citations in the corpus
- On cross-validated Lasso in high dimensions (2016, unknown): “5) [0, 5] [6, 10] [11, 15] [16, 20] [21, 25] [26, p] [31, p] [36, p] (n, p)=(100, 40) 0.”
- Nearly optimal central limit theorem and bootstrap approximations in high dimensions (2020, methodology): “in multiple hypothesis testing with the family-wise error rate control and in selecting penalty parameters for regularized estimators of high-dimensional models; see [6] for details on these and other examples.”
- Improved central limit theorem and bootstrap approximations in high dimensions (2019, unknown): “in [3].”