We investigate controlling false discovery rate (FDR) under dependence. Our main result is a generalization of the results obtained by Genovese and Wasserman (2004) and Farcomeni (2007).
Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.
The paper considers the problem of consistent variable selection in parametic models with the use of stepdown multiple hypothesis procedures. Our approach completes the results of Bunea et al. [J. Statist. Plann. Inference 136 (2006)]. A simulation study supports the results obtained.
We consider the problem of simultaneous testing of a finite number of null hypotheses , i=1,...,s. Starting from the classical paper of Lehmann (1957), it has become a very popular subject of research. In many applications, particularly in molecular biology (see e.g. Dudoit et al. (2003), Pollard et al. (2005)), the number s, i.e. the number of tested hypotheses, is large and the popular procedures that control the familywise error rate (FWERM) have small power. Therefore, we are concerned with...
Our goal is to state and prove the almost sure central limit theorem for maxima (Mn) of X1, X2, ..., Xn, n ∈ ℕ, where (Xi) forms a stochastic process of identically distributed r.v.’s of the continuous type, such that, for any fixed n, the family of r.v.’s (X1, ...,Xn) has the Archimedean copula CΨ.
In our paper, we consider different approaches to the problem of simultaneous testing of many null hypotheses. In this context, we discuss the single-step, the step-down and the step-up procedures of multiple testing. In particular, we are concerned with their properties and applications in the control of the error rates, such as:FW ER, k-FWER, FDP, FDR, pFDR. The mentioned procedures are intensively used in the DNA microarrays analysis, which enables the monitoring of expression levels of many...
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