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 other approaches is the use of flexible functional dependence measure to quantify dependence. A central limit theorem and nonasymptotic maximal inequalities are provided. The used prove convergence distribution (EDF) derive uniform rates kernel density estimators both processes. comparison with earlier results based on measures carried out.