A1050
Title: Two-sample testing with a graph-based total variation integral probability metric
Authors: Alden Green - Stanford University (United States) [presenting]
Abstract: A novel multivariate nonparametric two-sample testing problem is considered where, under the alternative, distributions $P$ and $Q$ are separated in an integral probability metric over functions of bounded total variation (TV IPM). A new test, the graph TV test, is proposed, and it uses a graph-based approximation to the TV IPM as its test statistic. It is shown that this test, computed with an $\varepsilon$-neighborhood graph and calibrated by permutation, is minimax rate-optimal for detecting alternatives separated in the TV IPM. As an important special case, it is shown that this implies the graph TV test is optimal for detecting spatially localized alternatives, whereas the $\chi^2$ test is probably suboptimal. The theory is supported by numerical experiments on simulated and real data.
