Non-asymptotic theory for nonparametric testing

Understand

We consider nonparametric testing in a non-asymptotic framework.

• Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size.
• Meanwhile, one proposed test is shown to achieve minimax optimality in the asymptotic sense.
• An important consequence of this non-asymptotic theory is a new and practically useful formula for selecting the optimal smoothing parameter in nonparametric testing.