Alexandre Belloni, Victor Chernozhukov, Denis Chetverikov, Christian Hansen, Kengo Kato
arXiv 5 Jun 2018 · Mathematics — Statistics Theory · 67 citations (OpenAlex)
arXiv:1806.01888 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Belloni, A., Chen, D., Chernozhukov, V. and Hansen, C (2012) Sparse models and methods for optimal instruments with an application to eminent domain self | 1.000 | 5 | 3 | 100% |
| 2 | Liu, W. and Shao, Q.-M (2014) Phase transition and regularized bootstrap in large-scale $t$-tests with false discovery rate control | 0.928 | 10 | 3 | 80% |
| 3 | Chernozhukov, V., Hansen, C. and Spindler M (2015) Valid post-selection and post-regularization inference: An elementary, general approach self | 0.928 | 4 | 3 | 100% |
| 4 | Candès, E. and Tao, E (2007) The Dantzig selector: statistical estimation when $p$ is much larger than $n$ | 0.928 | 4 | 3 | 100% |
| 5 | Belloni, A., Chernozhukov, V., Hansen, C., and Newey, W (2017) Simultaneous confidence intervals for high-dimensional linear models with many endogenous variables self | 0.894 | 7 | 4 | 71% |
| 6 | Chernozhukov, V., Chetverikov, D. and Kato, K (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors self | 0.874 | 12 | 2 | 100% |
| 7 | Belloni, A., Chernozhukov, V. and Kato, K (2015) Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems self | 0.874 | 6 | 2 | 100% |
| 8 | Chernozhukov, V., Chetverikov, D. and Kato, K (2015) Comparison and anti-concentration bounds for maxima of Gaussian random vectors self | 0.754 | 7 | 4 | 43% |
| 9 | Chernozhukov, V., Chetverikov, D. and Kato, K (2017) Central limit theorems and bootstrap in high dimensions self | 0.744 | 17 | 3 | 41% |
| 10 | Belloni, A. and Chernozhukov, V (2011) $_1$-penalized quantile regression in high-dimensional sparse models self | 0.737 | 3 | 3 | 67% |
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