Testing over a continuum of null hypotheses with False Discovery Rate control
Abstract
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding -value) is known for each individual hypothesis. We extend to this setting the notion of false discovery rate (FDR) as a measure of type I error. Our main result studies specific procedures based on the observation of the -value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of -values, or under the assumption that the finite dimensional distributions of the -value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting. Its interest is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables.
Cite
@article{arxiv.1110.3599,
title = {Testing over a continuum of null hypotheses with False Discovery Rate control},
author = {Gilles Blanchard and Sylvain Delattre and Etienne Roquain},
journal= {arXiv preprint arXiv:1110.3599},
year = {2014}
}