In this paper we show that a path-wise solution to the following integral equation Yt = ∫ t 0 f(Yt) dXt Y0 = a ∈ R d exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α > p. There are two types of solution, determined by the solution’s behaviour at jump times of the process X, one we call geometric the other...

The present article proposes general single-step multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors, such as the generalized family-wise error rate. A key feature of our approach is the test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rej...

It is common in econometric applications that several hypothesis tests are carried out simultaneously. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. The classical approach is to control the familywise error rate (FWE) which is the probability of one or more false rejections. But when the number of hypotheses under consideration is larg...

Procedures controlling error rates measuring at least k false rejections, instead of at least one, can potentially increase the ability of a procedure to detect false null hypotheses in situations where one seeks to control k or more false rejections having tolerated a few of them. The k-FWER, which is the probability of at least k false rejections and generalizes the usual familywise error rat...

In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by generalizing it to control the k-FWER, the probability of falsely rejecting at least k null hypotheses, for some fixed k > 1. Simes’ test for testing the intersection n...

Graphical approaches have been proposed in the literature for testing hypotheses on multiple endpoints by recycling significance levels from rejected hypotheses to unrejected ones. Recently, they have been extended to group sequential procedures (GSPs). Our focus in this paper is on the allocation of recycled significance levels from rejected hypotheses to the stages of the GSPs for unrejected ...

Consider the problem of simultaneously testing null hypotheses H1, . . . ,Hs. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. In many applications, particularly if s is large, one might be willing to tolerate more than one false rejection provided the nu...

Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering point-wise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical applications, such large sets of solutions express equally relevant alternatives which need to be ident...

The concept of k-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections, for some fixed k ≥ 1. A less conservative notion, the k-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394–415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 5...