Distribution-free two-sample testing with blurred total variation distance
This work addresses the challenge of certifying distribution equality or bounding distances in a distribution-free regime, which is significant for statistical inference when assumptions cannot be made, though it appears incremental as it builds on existing total variation concepts.
The paper tackles the problem of two-sample testing without distributional assumptions by introducing the blurred total variation distance, a relaxation that enables inference where traditional methods fail. They provide theoretical guarantees for distribution-free bounds on this distance and analyze its properties in high-dimensional settings.
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.