Empirical process theory for nonsmooth functions under functional dependence
We provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A functional central limit theorem and nonasymptotic maximal inequaliti...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
18 May 2022
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| In: |
Electronic journal of statistics
Year: 2022, Volume: 16, Issue: 1, Pages: 3385-3429 |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/22-EJS2023 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1214/22-EJS2023 Verlag, kostenfrei, Volltext: https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-16/issue-1/Empirical-process-theory-for-nonsmooth-functions-under-functional-dependence/10.1214/22-EJS2023.full 
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| Author Notes: | Nathawut Phandoidaen and Stefan Richter |
| Summary: | We provide an empirical process theory for locally stationary processes over nonsmooth function classes. An important novelty over other approaches is the use of the flexible functional dependence measure to quantify dependence. A functional central limit theorem and nonasymptotic maximal inequalities are provided. The theory is used to prove the functional convergence of the empirical distribution function (EDF) and to derive uniform convergence rates for kernel density estimators both for stationary and locally stationary processes. A comparison with earlier results based on other measures of dependence is carried out. |
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| Item Description: | Gesehen am 30.08.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1935-7524 |
| DOI: | 10.1214/22-EJS2023 |