Consistency of model-based bootstrap methods for degenerate U- and V -type statistics

by    A. Leucht, M. H. Neumann

Preprint series: 08-03, Reports on Stochastics and Statistics

A. Leucht, M. H. Neumann

62G09 Resampling methods
62F40 Bootstrap, jackknife and other resampling methods
62G20 Asymptotic properties
62F05 Asymptotic properties of tests

Abstract: We provide general results on the consistency of certain bootstrap methods applied to degree-2 degenerate statistics of U- and V -type. While it follows from well known results that the original statistic converges in distribution to a weighted sum of centered chisquared random variables, a direct proof for the bootstrap counterpart can be difficult for several reasons. We employ simple coupling arguments to show that the bootstrap statistic converges to the same limit as the original one.

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

Upload: 2008-03-12

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