ADAPTIVE TESTING ON A REGRESSION FUNCTION AT A POINT

作者：Armstrong Timothy^*

来源：Annals of Statistics, 2015, 43(5): 2086-2101.

DOI：10.1214/15-AOS1342

• Adaptive testing
• regression discontinuity
• identification at infinity

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.

• 出版日期2015-10