Related papers: Adaptive FDR control under independence and depend…
In multiple hypothesis testing, it is well known that adaptive procedures can enhance power via incorporating information about the number of true nulls present. Under independence, we establish that two adaptive false discovery rate (FDR)…
In the multiple testing problem with independent tests, the classical linear step-up procedure controls the false discovery rate (FDR) at level $\pi_0\alpha$, where $\pi_0$ is the proportion of true null hypotheses and $\alpha$ is the…
Efforts to develop more efficient multiple hypothesis testing procedures for false discovery rate (FDR) control have focused on incorporating an estimate of the proportion of true null hypotheses (such procedures are called adaptive) or…
In this work we study an adaptive step-down procedure for testing $m$ hypotheses. It stems from the repeated use of the false discovery rate controlling the linear step-up procedure (sometimes called BH), and makes use of the critical…
We investigate the performance of a family of multiple comparison procedures for strong control of the False Discovery Rate ($\mathsf{FDR}$). The $\mathsf{FDR}$ is the expected False Discovery Proportion ($\mathsf{FDP}$), that is, the…
The present paper introduces new adaptive multiple tests which rely on the estimation of the number of true null hypotheses and which control the false discovery rate (FDR) at level alpha for finite sample size. We derive exact formulas for…
Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false…
Inequalities are key tools to prove FDR control of a multiple test. The present paper studies upper and lower bounds for the FDR under various dependence structures of p-values, namely independence, reverse martingale dependence and…
As the volume and complexity of data continue to expand across various scientific disciplines, the need for robust methods to account for the multiplicity of comparisons has grown widespread. A popular measure of type 1 error rate in…
Multiple testing with false discovery rate (FDR) control has been widely conducted in the ``discrete paradigm" where p-values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose…
Multiple hypothesis testing often involves composite nulls, i.e., nulls that are associated with two or more distributions. In many cases, it is reasonable to assume that there is a prior distribution on the distributions despite it is…
In many scientific settings there is a need for adaptive experimental design to guide the process of identifying regions of the search space that contain as many true positives as possible subject to a low rate of false discoveries (i.e.…
Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these…
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,…
We consider multiple testing with false discovery rate (FDR) control when p-values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less…
We consider the problem of multiple hypothesis testing with generic side information: for each hypothesis $H_i$ we observe both a p-value $p_i$ and some predictor $x_i$ encoding contextual information about the hypothesis. For large-scale…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
The most popular multiple testing procedures are stepwise procedures based on $P$-values for individual test statistics. Included among these are the false discovery rate (FDR) controlling procedures of Benjamini--Hochberg [J. Roy. Statist.…
In this paper we introduce and investigate a new rejection curve for asymptotic control of the false discovery rate (FDR) in multiple hypotheses testing problems. We first give a heuristic motivation for this new curve and propose some…
This research deals with massive multiple hypothesis testing. First regarding multiple tests as an estimation problem under a proper population model, an error measurement called Erroneous Rejection Ratio (ERR) is introduced and related to…