Degenerate U- and V-statistics under weak dependence: Asymptotic theory and bootstrap consistency

by    A. Leucht

Preprint series: 10-05, Reports on Stochastics and Statistics

62E20 Asymptotic distribution theory
62G09 Resampling methods

Abstract: We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose we derive the limit
distributions of degree-2 degenerate U- and V-statistics for weakly dependent $R^d$-valued random variables first. To this end, only some moment conditions and smoothness assumptions
concerning the kernel are required. Based on this result, we verify that the bootstrap counterparts of these statistics converge to the same limit distributions. Finally, some
applications to hypothesis testing are presented.

Keywords: Bootstrap, consistency, U-statistics, V -statistics, weak dependence

Upload: 2010-08-11

Update: 2011 -05 -03

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