Publication Date: August 2014
Revision Date: October 2014February 2015
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.
Adaptive inference, Regression discontinuity, Identiﬁcation at inﬁnity
JEL Classification Codes: C14, C12
Published in The Annals of Statistics (October 2015), 43(5), 2086–2101 [DOI]