{"ID":2850117,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22792","arxiv_id":"2510.22792","title":"Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters","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 $χ^2$-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 $U$-statistics and use it to derive a new Kernel Stein Discrepancy composite goodness-of-fit test.","short_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 optim...","url_abs":"https://arxiv.org/abs/2510.22792","url_pdf":"https://arxiv.org/pdf/2510.22792v2","authors":"[\"Florian Brück\",\"Veronika Reimoser\",\"Fabian Baier\"]","published":"2025-10-26T18:50:43Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}