Maximal Inequalities for Empirical Processes under General Mixing Conditions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914421738045440 |
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| author | Pouzo, Demian |
| author_facet | Pouzo, Demian |
| contents | This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a concentration rate and a novel measure of complexity. The speed of mixing, however, affects the former quantity implying a phase transition. Fast mixing leads to the standard root-n concentration rate, while slow mixing leads to a slower concentration rate whose speed depends on the mixing structure. Our findings are applied to obtain new Glivenko-Cantelli type results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Inequalities for Empirical Processes under General Mixing Conditions Pouzo, Demian Probability Econometrics Statistics Theory Primary 60F15, 60F99, 60E15, secondary 60F17 This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a concentration rate and a novel measure of complexity. The speed of mixing, however, affects the former quantity implying a phase transition. Fast mixing leads to the standard root-n concentration rate, while slow mixing leads to a slower concentration rate whose speed depends on the mixing structure. Our findings are applied to obtain new Glivenko-Cantelli type results. |
| title | Maximal Inequalities for Empirical Processes under General Mixing Conditions |
| topic | Probability Econometrics Statistics Theory Primary 60F15, 60F99, 60E15, secondary 60F17 |
| url | https://arxiv.org/abs/2402.11394 |