无需分布的两样本检验与模糊总变差距离
Distribution-free two-sample testing with blurred total variation distance
AI总结：
本文提出模糊总变差距离用于无需分布假设的两样本检验，提供理论保障并探讨其高维性质。
摘要：
两样本检验旨在根据每个分布的样本判断两个分布是否相等。在无法对分布性质做假设时，确定分布相等或提供总变差（TV）距离的紧上界是无法实现的。本文研究了模糊TV距离，这是TV距离的放松形式，允许在不假设分布的情况下进行推断。我们为模糊TV距离提供了分布无关的上界和下界理论保证，并探讨了其在高维中的性质。
英文摘要：
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular, certifying equality of distributions, or even providing a tight upper bound on the total variation (TV) distance between the distributions, is impossible to achieve in a distribution-free regime. In this work, we examine the blurred TV distance, a relaxation of TV distance that enables us to perform inference without assumptions on the distributions. We provide theoretical guarantees for distribution-free upper and lower bounds on the blurred TV distance, and examine its properties in high dimensions.
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