Nonparametric Two-Sample Testing by Betting

Understand

We study the problem of designing consistent sequential two-sample tests in a nonparametric setting.

• Guided by the principle of testing by betting, we reframe this task into that of selecting a sequence of payoff functions that maximize the wealth of a fictitious bettor, betting against the null in a repeated game.
• In this setting, the relative increase in the bettor's wealth has a precise interpretation as the measure of evidence against the null, and thus our sequential test rejects the null when the wealth crosses an appropriate threshold.
• We develop a general framework for setting up the betting game for two-sample testing, in which the payoffs are selected by a prediction strategy as data-driven predictable estimates of the witness function associated with the variational representation of some statistical distance measures, such as integral probability metrics (IPMs).