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A wild bootstrap method for nonparametric hypothesis tests based on kerneldistribution embeddings is proposed. This bootstrap method is used to constructprovably consistent tests that apply to random processes, for which the naivepermutation-based bootstrap fails. It applies to a large group of kernel testsbased on V-statistics, which are degenerate under the null hypothesis, andnon-degenerate elsewhere. To illustrate this approach, we construct atwo-sample test, an instantaneous independence test and a multiple lagindependence test for time series. In experiments, the wild bootstrap givesstrong performance on synthetic examples, on audio data, and in performancebenchmarking for the Gibbs sampler.

A Wild Bootstrap for Degenerate Kernel Tests