Bootstrap for dependent Hilbert space-valued random variables with application to von Mises statistics
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Date
2014-03-25
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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.
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Keywords
absolute regularity, functional time series, block bootstrap, Hilbert space, near epoch dependence