B0987
Title: Minimax goodness-of-fit testing in Wasserstein distance
Authors: Tudor Manole - Carnegie Mellon University (United States) [presenting]
Sivaraman Balakrishnan - Carnegie Mellon University (United States)
Larry Wasserman - Carnegie Mellon University (United States)
Abstract: The goodness-of-fit problem of testing whether a sample arose from a given distribution is considered against a composite alternative separated from the null in Wasserstein distance. The minimax perspective is adopted and seeks to find the critical testing radius for this problem under various assumptions on the set of alternatives. Two contributions are made. First, absent any smoothness assumptions, it is shown that the critical radius for this problem is faster than the corresponding Wasserstein two-sample testing critical radius, which was derived in prior studies. This suggests that the Wasserstein two-sample testing problem is statistically harder than its one-sample counterpart, contrary to the related problem of estimating the Wasserstein distance, for which the one- and two-sample minimax rates coincide. Second, it is shown that several commonly-used test statistics are minimax-optimal for goodness-of-fit testing in Wasserstein distance, under appropriate smoothness assumptions and tuning.
