A Wild Bootstrap for Degenerate Kernel Tests

TL;DR

This paper introduces a wild bootstrap method for nonparametric kernel tests that remain valid for complex, degenerate cases where traditional permutation methods fail, enhancing the reliability of hypothesis testing in stochastic processes.

Contribution

The paper presents a novel wild bootstrap approach for kernel-based hypothesis tests applicable to degenerate cases, improving test validity for time series and other stochastic data.

Findings

Strong performance on synthetic data

Effective in audio data analysis

Benchmark results for Gibbs sampler

Abstract

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.