MMD Aggregated Two-Sample Test

Understand

We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD).

• First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to determine the test threshold.
• We prove that this test controls the probability of type I error non-asymptotically.
• Hence, it can be used reliably even in settings with small sample sizes as it remains well-calibrated, which differs from previous MMD tests which only guarantee correct test level asymptotically.