Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of func...
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| Format: | Article |
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Elsevier BV
2018
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| Online Access: | http://hdl.handle.net/1721.1/119502 https://orcid.org/0000-0002-3250-6714 |
| _version_ | 1826205034147217408 |
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| author | Chetverikov, Denis Kato, Kengo Chernozhukov, Victor V |
| author2 | Massachusetts Institute of Technology. Department of Economics |
| author_facet | Massachusetts Institute of Technology. Department of Economics Chetverikov, Denis Kato, Kengo Chernozhukov, Victor V |
| author_sort | Chetverikov, Denis |
| collection | MIT |
| description | We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian–Stein methods and Gaussian comparison inequalities. The increasing complexity of classes of functions and non-centrality of the processes make the results useful for applications in modern nonparametric statistics (Giné and Nickl 2015), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations. Keywords: Coupling, Empirical process, Multiplier bootstrap process, Empirical bootstrap process, Gaussian approximation, Supremum |
| first_indexed | 2024-09-23T13:05:41Z |
| format | Article |
| id | mit-1721.1/119502 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:05:41Z |
| publishDate | 2018 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1195022022-10-01T13:01:18Z Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings Chetverikov, Denis Kato, Kengo Chernozhukov, Victor V Massachusetts Institute of Technology. Department of Economics Chernozhukov, Victor V We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian–Stein methods and Gaussian comparison inequalities. The increasing complexity of classes of functions and non-centrality of the processes make the results useful for applications in modern nonparametric statistics (Giné and Nickl 2015), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations. Keywords: Coupling, Empirical process, Multiplier bootstrap process, Empirical bootstrap process, Gaussian approximation, Supremum National Science Foundation (U.S.) 2018-12-11T15:52:38Z 2018-12-11T15:52:38Z 2016-04 2015-01 2018-12-04T13:40:51Z Article http://purl.org/eprint/type/JournalArticle 0304-4149 http://hdl.handle.net/1721.1/119502 Chernozhukov, Victor, Denis Chetverikov, and Kengo Kato. “Empirical and Multiplier Bootstraps for Suprema of Empirical Processes of Increasing Complexity, and Related Gaussian Couplings.” Stochastic Processes and Their Applications 126, no. 12 (December 2016): 3632–3651. https://orcid.org/0000-0002-3250-6714 http://dx.doi.org/10.1016/J.SPA.2016.04.009 Stochastic Processes and their Applications Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Chetverikov, Denis Kato, Kengo Chernozhukov, Victor V Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title | Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title_full | Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title_fullStr | Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title_full_unstemmed | Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title_short | Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings |
| title_sort | empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity and related gaussian couplings |
| url | http://hdl.handle.net/1721.1/119502 https://orcid.org/0000-0002-3250-6714 |
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