Testing over a continuum of null hypotheses with False Discovery Rate control

作者：Blanchard Gilles^*; Delattre Sylvain; Roquain Etienne

来源：Bernoulli, 2014, 20(1): 304-333.

DOI：10.3150/12-BEJ488

• continuous testing
• false discovery rate
• multiple testing
• positive correlation
• step-up
• stochastic process

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 p-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 p-value process. Control of the FDR at a nominal level is ensured either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-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.

• 出版日期2014-2