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Dependent wild bootstrap for the empirical process. (English) Zbl 1325.62065

Summary: 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 X. Shao [J. Am. Stat. Assoc. 105, No. 489, 218–235 (2010; Zbl 1397.62121)] 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.

MSC:

62F40 Bootstrap, jackknife and other resampling methods
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 1397.62121

Software:

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References:

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