by A. Leucht, M. H. Neumann
Preprint series: 08-03, Reports on Stochastics and Statistics
A. Leucht, M. H. Neumann
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