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

Authors:
Anne Leucht;Michael H. Neumann
Affiliations:
Friedrich-Schiller-Universität Jena, Institut für Stochastik, Ernst-Abbe-Platz 2, D-07743 Jena, Germany;Friedrich-Schiller-Universität Jena, Institut für Stochastik, Ernst-Abbe-Platz 2, D-07743 Jena, Germany
Venue:
Journal of Multivariate Analysis
Year:
2009

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Abstract

We provide general results on the consistency of certain bootstrap methods applied to degree-2 degenerate statistics of U-type and V-type. While it follows from well known results that the original statistic converges in distribution to a weighted sum of centred chi-squared random variables, we use a coupling idea of Dehling and Mikosch to show that the bootstrap counterpart converges to the same distribution. The result is applied to a goodness-of-fit test based on the empirical characteristic function.