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Our test statistic is based on an empirical estimate of this\ndivergence, taking the form of a V-statistic in terms of the log gradients of\nthe target density and the kernel. We derive a statistical test, both for\ni.i.d. and non-i.i.d. samples, where we estimate the null distribution\nquantiles using a wild bootstrap procedure. We apply our test to quantifying\nconvergence of approximate Markov Chain Monte Carlo methods, statistical model\ncriticism, and evaluating quality of fit vs model complexity in nonparametric\ndensity estimation.","url_abs":"http://arxiv.org/abs/1602.02964v4","url_pdf":"http://arxiv.org/pdf/1602.02964v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-kernel-test-of-goodness-of-fit","repo_url":"https://github.com/karlnapf/kernel_goodness_of_fit","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"density-estimation","task_name":"Density Estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1602.02964","atlas_url":"https://app.syntology.ai/?focus=1602.02964","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1602.02964"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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