Open Access
2022 Empirical process theory for nonsmooth functions under functional dependence
Nathawut Phandoidaen, Stefan Richter
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Electron. J. Statist. 16(1): 3385-3429 (2022). DOI: 10.1214/22-EJS2023


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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Nathawut Phandoidaen. Stefan Richter. "Empirical process theory for nonsmooth functions under functional dependence." Electron. J. Statist. 16 (1) 3385 - 3429, 2022.


Received: 1 August 2021; Published: 2022
First available in Project Euclid: 18 May 2022

MathSciNet: MR4423798
zbMATH: 1497.60047
Digital Object Identifier: 10.1214/22-EJS2023

Keywords: Empirical process theory , functional central limit theorem , functional dependence measure , Locally stationary processes , maximal inequality

Vol.16 • No. 1 • 2022
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