Non-asymptotic Analysis for Nonparametric Testing

Document Type

Conference Proceeding

Publication Date

1-1-2020

Abstract

We develop a non-asymptotic framework for hypothesis testing in nonparametric regression where the true regression function belongs to a Sobolev space. 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 rate 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 the testing statistic. Extensions of our results to general reproducing kernel Hilbert spaces and non-Gaussian error regression are also discussed.

Identifier

85161282096 (Scopus)

Publication Title

Proceedings of Machine Learning Research

e-ISSN

26403498

First Page

3709

Last Page

3755

Volume

125

Grant

DMS-1712907

Fund Ref

National Science Foundation

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