CFDP 1957R

Adaptive Testing on a Regression Function at a Point


Publication Date: August 2014

Revision Date: October 2014February 2015

Pages: 19


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]