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

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 distribution of degree-2 degenerate U and V -statistics for weakly dependent Rd-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. 2000 Mathematics Subject Classification. 62E20, 62G09.