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October 2015 Adaptive testing on a regression function at a point
Timothy Armstrong
Ann. Statist. 43(5): 2086-2101 (October 2015). DOI: 10.1214/15-AOS1342


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.


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Timothy Armstrong. "Adaptive testing on a regression function at a point." Ann. Statist. 43 (5) 2086 - 2101, October 2015.


Received: 1 October 2014; Revised: 1 February 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 1327.62276
MathSciNet: MR3375877
Digital Object Identifier: 10.1214/15-AOS1342

Primary: 62G08 , 62G10
Secondary: 62G20

Keywords: Adaptive testing , identification at infinity , regression discontinuity

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 5 • October 2015
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