A Wild Bootstrap for Degenerate Kernel Tests
This work addresses a methodological gap for statisticians and machine learning practitioners dealing with degenerate kernel tests in time series and random processes, though it is incremental as it builds on existing kernel test frameworks.
The authors tackled the problem of nonparametric hypothesis tests for random processes using kernel distribution embeddings, where naive permutation-based bootstraps fail, by proposing a wild bootstrap method that yields provably consistent tests and demonstrates strong performance on synthetic examples, audio data, and Gibbs sampler benchmarking.
A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on V-statistics, which are degenerate under the null hypothesis, and non-degenerate elsewhere. To illustrate this approach, we construct a two-sample test, an instantaneous independence test and a multiple lag independence test for time series. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler.