Adaptive testing on a regression function at a point
The Annals of Statistics · 2015 · Volume 43 · Issue 5
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.
Keywords
62G08, 62G10, 62G20, Adaptive testing, identification at infinity, regression discontinuity
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