Document Type
Discussion Paper
Publication Date
8-1-2014
CFDP Number
1957R
CFDP Revision Date
2015-02-01
CFDP Pages
19
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.
Recommended Citation
Armstrong, Timothy B., "Adaptive Testing on a Regression Function at a Point" (2014). Cowles Foundation Discussion Papers. 2366.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/2366