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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.22792 |
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| _version_ | 1866915810606317568 |
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| author | Brück, Florian Reimoser, Veronika Baier, Fabian |
| author_facet | Brück, Florian Reimoser, Veronika Baier, Fabian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22792 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters Brück, Florian Reimoser, Veronika Baier, Fabian Statistics Theory 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. |
| title | Composite goodness-of-fit test with the Kernel Stein Discrepancy and a bootstrap for degenerate U-statistics with estimated parameters |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2510.22792 |