Minimax Optimal Goodness-of-Fit Testing with Kernel Stein Discrepancy

arXiv:2404.08278v1 Announce Type: cross
Abstract: We explore the minimax optimality of goodness-of-fit tests on general domains using the kernelized Stein discrepancy (KSD). The KSD framework offers a flexible approach for goodness-of-fit testing, avoiding strong distributional assumptions, accommodating diverse data structures beyond Euclidean spaces, and relying only on partial knowledge of the reference distribution, while maintaining computational efficiency. We establish a general framework and an operator-theoretic representation of the KSD, encompassing many existing KSD tests in the literature, which vary depending …

abstract arxiv assumptions beyond data diverse domains explore framework general kernel knowledge math.st minimax reference spaces stat.ml stat.th testing tests type