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We provide an empirical process theory for locally stationary processes overnonsmooth function classes. An important novelty over other approaches is theuse of the flexible functional dependence measure to quantify dependence. Afunctional central limit theorem and nonasymptotic maximal inequalities areprovided. The theory is used to prove the functional convergence of theempirical distribution function (EDF) and to derive uniform convergence ratesfor kernel density estimators both for stationary and locally stationaryprocesses. A comparison with earlier results based on other measures ofdependence is carried out.

Empirical process theory for nonsmooth functions under functional dependence