Kernel Tests of Equivalence
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Abstract (arXiv)
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null hypothesis may simply be a result of lack of test power, also known as the Type-II error. This motivates equivalence testing, which aims to assess the absence of a statistically meaningful effect under controlled error rates. However, existing equivalence tests are either limited to parametric distributions or focus only on specific moments rather than the full distribution. We address these limitations using two kernel-based statistical discrepancies: the kernel Stein discrepancy and the Maximum Mean Discrepancy. The null hypothesis of our proposed tests assumes the candidate distribution differs from the nominal distribution by at least a pre-defined margin, which is measured by these discrepancies. We propose two approaches for computing the critical values of the tests, one using an asymptotic normality approximation, and another based on bootstrapping. Numerical experiments are conducted to assess the performance of these tests.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 30 of its 104 references that are in the map. First posted on arXiv 11 Mar 2026.
Builds on
30 of 104 references.
References · 30
- 2017Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methodscited by 546
- 2019The frontier of simulation-based inferencecited by 502
- 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
- 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
- 2016A Kernel Test of Goodness of Fitcited by 143
- 2020Learning Deep Kernels for Non-Parametric Two-Sample Testscited by 130
- 2017Measuring Sample Quality with Kernelscited by 119
- 2021MMD Aggregated Two-Sample Testcited by 75
- 2014Control functionals for Monte Carlo integrationcited by 59
- 2017A Linear-Time Kernel Goodness-of-Fit Testcited by 41
- 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 36
- 2021Stein's Method Meets Computational Statistics: A Review of Some Recent Developmentscited by 32
18 more
- 2015A Test of Relative Similarity For Model Selection in Generative Modelscited by 25
- 2022A Finite-Particle Convergence Rate for Stein Variational Gradient Descentcited by 22
- 2022KSD Aggregated Goodness-of-fit Testcited by 21
- 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
- 2021Composite Goodness-of-fit Tests with Kernelscited by 16
- 2024Credal Two-Sample Tests of Epistemic Uncertaintycited by 16
- 2022Targeted Separation and Convergence with Kernel Discrepanciescited by 15
- 2020Dimension-agnostic inference using cross U-statisticscited by 14
- 2020A Stein Goodness-of-fit Test for Directional Distributionscited by 13
- 2020Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Datacited by 12
- 2018Informative Features for Model Comparisoncited by 9
- 2020A General Method for Calibrating Stochastic Radio Channel Models with Kernelscited by 9
- 2024Robust Kernel Hypothesis Testing under Data Corruptioncited by 7
- 2024On the Robustness of Kernel Goodness-of-Fit Testscited by 7
- 2022Kernel Robust Hypothesis Testingcited by 6
- 2023A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testingcited by 5
- 2023Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancycited by 4
- 2021Testing semiparametric model-equivalence hypotheses based on the characteristic functioncited by 1
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Citing papers per year: 2026: 2.
2 papers.