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Empirical process theory for nonsmooth functions under functional dependence. (English) Zbl 1497.60047

The authors provide an empirical process theory for locally stationary processes over nonsmooth function classes and introduce a 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.

MSC:

60F17 Functional limit theorems; invariance principles
60F10 Large deviations
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