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A0274
Title: A unifying view on kernel stein discrepancy tests for goodness-of-fit Authors:  Wenkai Xu - University of Tuebingen (Germany) [presenting]
Abstract: Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. We introduce various KSD-based goodness-of-fit testing including Euclidean data, survival data, directional data and compositional data. Standardisation methods have been developed in Stein's method literature to study approximation properties for normal distributions. We apply techniques inspired by the standardisation idea that enable us to present a unifying view to theoretically compare and interpret different Stein operators in performing the KSD-based goodness-of-fit testing. The unifying framework is also useful as a guide to develop novel KSD-based tests. Different choice of standardisation functions results in different Stein operators, whose corresponding KSD choices have a considerable effect on the test performances. We discuss the operator choice and kernel choice for KSD-based testing procedures. We show experimental results demonstrate that these KSD tests control type-I error well and achieve higher test power than existing approaches, including the test based on maximum-mean-discrepancy (MMD).