  We consider a data-driven robust hypothesis test where the optimal test will
minimize the worst-case performance regarding distributions that are close to
the empirical distributions with respect to the Wasserstein distance. This
leads to a new non-parametric hypothesis testing framework based on
distributionally robust optimization, which is more robust when there are
limited samples for one or both hypotheses. Such a scenario often arises from
applications such as health care, online change-point detection, and anomaly
detection. We study the computational and statistical properties of the
proposed test by presenting a tractable convex reformulation of the original
infinite-dimensional variational problem exploiting Wasserstein's properties
and characterizing the radii selection for the uncertainty sets. We also
demonstrate the good performance of our method on synthetic and real data.
