Document Type

Discussion Paper

Publication Date

8-1-2014

CFDP Number

1957

CFDP Revision Date

2014-10-01

CFDP Pages

17

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 Holder 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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Economics Commons

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