The Annals of Statistics

Adaptive testing on a regression function at a point

Timothy Armstrong

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We consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null. We propose a test that achieves the optimal minimax rate adaptively over a range of Hölder classes, up to a $\log\log n$ term, which we show to be necessary for adaptation. We apply the results to adaptive one-sided tests for the regression discontinuity parameter under a monotonicity restriction, the value of a monotone regression function at the boundary and the proportion of true null hypotheses in a multiple testing problem.

Article information

Ann. Statist. Volume 43, Number 5 (2015), 2086-2101.

Received: October 2014
Revised: February 2015
First available in Project Euclid: 3 August 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties

Adaptive testing regression discontinuity identification at infinity


Armstrong, Timothy. Adaptive testing on a regression function at a point. Ann. Statist. 43 (2015), no. 5, 2086--2101. doi:10.1214/15-AOS1342.

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