TY  - JOUR
A1  - Blanchard, Gilles
A1  - Dickhaus, Thorsten
A1  - Roquain, Etienne
A1  - Villers, Fanny
T1  - On least favorable configurations for step-up-down tests
JF  - Statistica Sinica
KW  - False discovery rate
KW  - least favorable configuration
KW  - multiple testing;
Y1  - 2014
U6  - https://doi.org/10.5705/ss.2011.205
SN  - 1017-0405
SN  - 1996-8507
VL  - 24
IS  - 1
SP  - 1
EP  - U31
PB  - Statistica Sinica, Institute of Statistical Science, Academia Sinica
CY  - Taipei
ER  - 
TY  - INPR
A1  - Blanchard, Gilles
A1  - Delattre, Sylvain
A1  - Roquain, Étienne
T1  - Testing over a continuum of null hypotheses
N2  - We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, 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, the latter one leading to a less conservative procedure. The interest of this approach 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. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 1 
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56877
ER  - 
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  -