Dependent Wild Bootstrap for the Empirical Process

Abstract

In this paper, we propose a model‐free bootstrap method for the empirical process under absolute regularity. More precisely, consistency of an adapted version of the so‐called dependent wild bootstrap, which was introduced by Shao () and is very easy to implement, is proved under minimal conditions on the tuning parameter of the procedure. We show how our results can be applied to construct confidence intervals for unknown parameters and to approximate critical values for statistical tests. In a simulation study, we investigate the size properties of a bootstrap‐aided Kolmogorov‐Smirnov test and show that our method is competitive to standard block bootstrap methods in finite samples.