# A Wild Bootstrap for Degenerate Kernel Tests

arXiv: https://arxiv.org/abs/1408.5404 · HTML: https://mlsanity.com/paper/1408.5404/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2014.

## Built on by (most cited first, 29 of 29)

- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [KSD Aggregated Goodness-of-fit Test](https://mlsanity.com/paper/2202.00824/) (2022)
- [Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancy](https://mlsanity.com/paper/2402.16041/) (2024)
- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Sequential Kernelized Independence Testing](https://mlsanity.com/paper/2212.07383/) (2022)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [On the Robustness of Kernel Goodness-of-Fit Tests](https://mlsanity.com/paper/2408.05854/) (2024)
- [Low-Rank Thinning](https://mlsanity.com/paper/2502.12063/) (2025)
- [Unveiling and Causalizing CoT: A Causal Pespective](https://mlsanity.com/paper/2502.18239/) (2025)
- [DUAL: Learning Diverse Kernels for Aggregated Two-sample and Independence Testing](https://mlsanity.com/paper/2510.11140/) (2025)
- [A Unified View of Optimal Kernel Hypothesis Testing](https://mlsanity.com/paper/2503.07084/) (2025)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [AgraSSt: Approximate Graph Stein Statistics for Interpretable Assessment of Implicit Graph Generators](https://mlsanity.com/paper/2203.03673/) (2022)
- [Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series](https://mlsanity.com/paper/2305.08529/) (2023)
- [Zero-Flow Two-Sample Tests](https://mlsanity.com/paper/2607.21542/) (2026)
- [A Stein Goodness of fit Test for Exponential Random Graph Models](https://mlsanity.com/paper/2103.00580/) (2021)
- [Adversarial Attack and Defense for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2202.03077/) (2022)
- [A general framework for the analysis of kernel-based tests](https://mlsanity.com/paper/2209.00124/) (2022)
- [Regularized f-Divergence Kernel Tests](https://mlsanity.com/paper/2601.19755/) (2026)
- [Estimating R'enyi's α-Cross-Entropies in a Matrix-Based Way](https://mlsanity.com/paper/2109.11737/) (2021)
- [A Kernelised Stein Statistic for Assessing Implicit Generative Models](https://mlsanity.com/paper/2206.00149/) (2022)
- [Non-Parametric Inference of Relational Dependence](https://mlsanity.com/paper/2207.00163/) (2022)
- [Probabilistic distances-based hallucination detection in LLMs with RAG](https://mlsanity.com/paper/2506.09886/) (2025)
- [Discussion of `Multiscale Fisher's Independence Test for Multivariate Dependence'](https://mlsanity.com/paper/2206.11142/) (2022)
- [Testing for Causal Fairness](https://mlsanity.com/paper/2502.12874/) (2025)
- [ProbRes: Volatility Learning for Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2606.02117/) (2026)
- [ASK-NN: An Asymmetric Nearest-Neighbor Test that detects Distribution Drifts in Natural Language](https://mlsanity.com/paper/2607.15607/) (2026)
- [Kernel-based External Validity of Experimental Studies](https://mlsanity.com/paper/2610.13625/) (2026)

## Abstract (arXiv)

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.