TY  - JOUR
A1  - Blanchard, Gilles
A1  - Delattre, Sylvain
A1  - Roquain, Etienne
T1  - Testing over a continuum of null hypotheses with False Discovery Rate control
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
N2  - 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.
KW  - continuous testing
KW  - false discovery rate
KW  - multiple testing
KW  - positive correlation
KW  - step-up
KW  - stochastic process
Y1  - 2014
U6  - https://doi.org/10.3150/12-BEJ488
SN  - 1350-7265
SN  - 1573-9759
VL  - 20
IS  - 1
SP  - 304
EP  - 333
PB  - International Statistical Institute
CY  - Voorburg
ER  -