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How to weigh the Benjamini-Hochberg procedure? In the context of multiple hypothesis testing, we propose a new step-wise procedure that controls the false discovery rate (FDR) and we prove it to be more powerful than any weighted Benjamini-Hochberg procedure. Both finite-sample and asymptotic results are presented. Moreover, we illustrate good performance… (More)

In the context of multiple hypotheses testing, the proportion π 0 of true null hypotheses among the hypotheses to test is a quantity that often plays a crucial role, although it is generally unknown. In order to obtain more powerful procedures, recent research has focused on finding ways to estimate this proportion and incorporate it in a meaningful way in… (More)

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a… (More)

We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call " self-consistency condition " , concerns the algorithm itself, and the second, called " dependency control condition " is related to the dependency assumptions on the p-value… (More)

This paper investigates an open issue related to false discovery rate (FDR) control of step-up-down (SUD) multiple testing procedures. It has been established in earlier literature that for this type of procedure, under some broad conditions, and in an asymptotical sense, the FDR is maximum when the signal strength under the alternative is maximum. In other… (More)

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution. The dimensionality of the vector can possibly be much larger than the number of observations and we focus on a… (More)

We study the control of the false discovery rate (FDR) for a general class of multiple testing procedures. We introduce a general condition, called " self-consistency " , on the set of hypotheses rejected by the procedure, which we show is sufficient to ensure the control of the corresponding false discovery rate under various conditions on the distribution… (More)

We study the properties of false discovery rate (FDR) thresh-olding, viewed as a classification procedure. The " 0 "-class (null) is assumed to have a known density while the " 1 "-class (alternative) is obtained from the " 0 "-class either by translation or by scaling. Furthermore , the " 1 "-class is assumed to have a small number of elements w.r.t. the "… (More)

In the context of correlated multiple tests, we aim to nonasymptotically control the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one-and two-sided multiple testing problem for the mean values of… (More)

In the context of correlated multiple tests, we aim at controlling non-asymptotically the family-wise error rate (FWER) using resampling-type procedures. We observe repeated realizations of a Gaussian random vector in possibly high dimension and with an unknown covariance matrix, and consider the one and two-sided multiple testing problem for the mean… (More)