Victor Chernozhukov, Denis Chetverikov, Kengo Kato, Yuta Koike
arXiv 22 Dec 2019 · Mathematics — Statistics Theory · publishedThe Annals of Statistics (2022) · 53 citations (OpenAlex)
arXiv:1912.10529 · PDF · DOI · OpenAlex · Extracted main text
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its distribution plays a key role in many high-dimensional econometric problems. Using a novel iterative randomized Lindeberg method, the paper derives new bounds for the distributional approximation errors. These new bounds substantially improve upon existing ones and simultaneously allow for a larger class of bootstrap methods.
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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 | Koike, Y (2021) Notes on the dimension dependence in high-dimensional central limit theorems for hyperrectangles self | 1.000 | 6 | 3 | 100% |
| 2 | Deng, H. and Zhang, C.-H (2020) Beyond Gaussian approximation: bootstrap for maxima of sums of independent random vectors | 0.950 | 14 | 4 | 86% |
| 3 | Chernozhukov, V., Chetverikov, D. and Kato, K (2017) Central limit theorems and bootstrap in high dimensions self | 0.888 | 10 | 6 | 70% |
| 4 | Chernozhukov, V., Chetverikov, D. and Kato, K (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors self | 0.830 | 7 | 5 | 57% |
| 5 | O'Donnell, R., Servedio, R., and Tan, L (2019) Fooling polytopes | 0.737 | 4 | 3 | 50% |
| 6 | Belloni, A., Chernozhukov, V., Chetverikov, D., Hansen, C., and Kato… (2018) High-dimensional econometrics and regularized GMM self | 0.737 | 3 | 2 | 100% |
| 7 | van der Vaart, A.W. and Wellner, J.A (1996) Weak Convergence and Empirical Processes: With Applications to Statistics | 0.644 | 3 | 2 | 67% |
| 8 | Koike, Y (2019) High-dimensional central limit theorems for homogeneous sums self | 0.644 | 2 | 2 | 100% |
| 9 | Mammen, E (1993) Bootstrap and wild bootstrap for high dimensional linear models | 0.644 | 2 | 2 | 100% |
| 10 | Chernozhukov, V., Chetverikov, D. and Kato, K (2015) Comparison and anti-concentration bounds for maxima of Gaussian random vectors self | 0.550 | 6 | 4 | 17% |
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