Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters
Statistics Theory
2026-02-24 v2 Statistics Theory
Abstract
This paper formally derives the asymptotic distribution of a goodness-of-fit test based on the Kernel Stein Discrepancy introduced in (Oscar Key et al., "Composite Goodness-of-fit Tests with Kernels", Journal of Machine Learning Research 26.51 (2025), pp. 1-60). The test enables the simultaneous estimation of the optimal parameter within a parametric family of candidate models. Its asymptotic distribution is shown to be a weighted sum of infinitely many -distributed random variables plus an additional disturbance term, which is due to the parameter estimation. Further, we provide a general framework to bootstrap degenerate parameter-dependent -statistics and use it to derive a new Kernel Stein Discrepancy composite goodness-of-fit test.
Cite
@article{arxiv.2510.22792,
title = {Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters},
author = {Florian Brück and Veronika Reimoser and Fabian Baier},
journal= {arXiv preprint arXiv:2510.22792},
year = {2026}
}