Authors: Dehling, Herold
Sharipov, Olimjon Sh.
Wendler, Martin
Title: Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics
Language (ISO): en
Abstract: Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the underlying process fulfills some mixing conditions. As parametric inference in an finite dimensional space is difficult, we show that the nonoverlapping block bootstrap is consistent. Furthermore, we show how these results can be used for degenerate von Mises-statistics.
Subject Headings: absolute regularity
functional time series
block bootstrap
Hilbert space
near epoch dependence
Issue Date: 2014-03-25
Appears in Collections:Sonderforschungsbereich (SFB) 823

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