A Wild Bootstrap for Degenerate Kernel Tests
arXiv:1408.5404
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.
References in corpus (4)
Cited by in corpus (15)
- Kernel Mean Embedding of Distributions: A Review and Beyond
- Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks
- A Kernel Test of Goodness of Fit
- Consistent distribution-free -sample and independence tests for univariate random variables
- FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test
- Kernelized Complete Conditional Stein Discrepancy
- Universal Hypothesis Testing with Kernels: Asymptotically Optimal Tests for Goodness of Fit
- Identifying Causal Structure in Dynamical Systems
- Composite Goodness-of-fit Tests with Kernels
- A kernel test for quasi-independence
- Asymptotically Optimal One- and Two-Sample Testing with Kernels
- A Stein Goodness of fit Test for Exponential Random Graph Models
- Interpretable Stein Goodness-of-fit Tests on Riemannian Manifolds
- A Kernel Two-sample Test for Dynamical Systems
- Estimating Rényi's -Cross-Entropies in a Matrix-Based Way