{"ID":2854839,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15058","arxiv_id":"2510.15058","title":"The Minimax Lower Bound of Kernel Stein Discrepancy Estimation","abstract":"Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\\sqrt n$-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is $n^{-1/2}$ and settling the optimality of these estimators. Our first result focuses on KSD estimation on $\\mathbb R^d$ with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality $d$. Our second result settles the minimax lower bound for KSD estimation on general domains.","short_abstract":"Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\\sqrt n$-convergence. In this work, we present two complementary results...","url_abs":"https://arxiv.org/abs/2510.15058","url_pdf":"https://arxiv.org/pdf/2510.15058v3","authors":"[\"Jose Cribeiro-Ramallo\",\"Agnideep Aich\",\"Florian Kalinke\",\"Ashit Baran Aich\",\"Zoltán Szabó\"]","published":"2025-10-16T18:16:05Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.ST\"]","methods":"[]","has_code":false}