The Annals of Statistics

Adaptive testing on a regression function at a point

Timothy Armstrong

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aos/1438606854

Digital Object Identifier
doi:10.1214/15-AOS1342

Mathematical Reviews number (MathSciNet)
MR3375877

Zentralblatt MATH identifier
1327.62276

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

Keywords
Adaptive testing regression discontinuity identification at infinity

Citation

Armstrong, Timothy. Adaptive testing on a regression function at a point. Ann. Statist. 43 (2015), no. 5, 2086--2101. doi:10.1214/15-AOS1342. https://projecteuclid.org/euclid.aos/1438606854


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