Degenerate U- and V-statistics under ergodicity: Asymptotics, bootstrap and applications in statistics

by    A. Leucht, M. H. Neumann

Preprint series: 11-01, Reports on Stochastics and Statistics

62E20 Asymptotic distribution theory
62M07 Non-Markovian processes: hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
60G10 Stationary processes

Abstract: We derive the asymptotic distributions of degenerate U- and V-statistics of stationary and
ergodic random variables. Statistics of these types naturally appear as approximations of
test statistics. Since the limit variables are of complicated structure, quantiles can hardly
be obtained directly. Therefore, we prove a general result on the consistency of model-based
bootstrap methods for U- and V-statistics under easily verifiable conditions. Finally, three
applications to hypothesis testing are presented.

Keywords: Bootstrap, ergodicity, U-statistic, V-statistic, Cram´er-von Mises-type test

Upload: 2011-05-04

Update: 2011 -05 -04

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