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Competition-based approach to controlling the false discovery rate (FDR) recently rose to prominence when, generalizing it to sequential hypothesis testing, Barber and Cand\`es used it as part of their knockoff-filter. Control of the FDR…
In the spirit of modeling inference for microarrays as multiple testing for sparse mixtures, we present a similar approach to a simplified version of quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the number of…
In this paper, we have attempted to study the behaviour of the family wise error rate (FWER) for Bonferroni's procedure and false discovery rate (FDR) of the Benjamini-Hodgeberg procedure for simultaneous testing problem with equicorrelated…
The mitigation of false positives is an important issue when conducting multiple hypothesis testing. The most popular paradigm for false positives mitigation in high-dimensional applications is via the control of the false discovery rate…
This article considers the problem of multiple hypothesis testing using $t$-tests. The observed data are assumed to be independently generated conditional on an underlying and unknown two-state hidden model. We propose an asymptotically…
We develop a technique to improve the power of any e-value by a simple randomization involving one independent uniform random variable. Using this framework, we show that two procedures for false discovery rate (FDR) control -- the…
The genetic basis of multiple phenotypes such as gene expression, metabolite levels, or imaging features is often investigated by testing a large collection of hypotheses, probing the existence of association between each of the traits and…
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…
Large-scale multiple testing with highly correlated test statistics arises frequently in many scientific research. Incorporating correlation information in estimating false discovery proportion has attracted increasing attention in recent…
Stability and reproducibility are essential considerations in various applications of statistical methods. False Discovery Rate (FDR) control methods are able to control false signals in scientific discoveries. However, many FDR control…
Several classical methods exist for controlling the false discovery exceedance (FDX) for large scale multiple testing problems, among them the Lehmann-Romano procedure ([LR] below) and the Guo-Romano procedure ([GR] below). While these two…
We provide new non-asymptotic false discovery proportion (FDP) confidence envelopes in several multiple testing settings relevant for modern high dimensional-data methods. We revisit the multiple testing scenarios considered in the recent…
We collect self-contained elementary proofs of four results in the literature on the false discovery rate of the Benjamini-Hochberg (BH) procedure for independent or positive-regression dependent p-values, the Benjamini-Yekutieli correction…
Given $m$ unknown parameters with corresponding independent estimators, the Benjamini-Hochberg (BH) procedure can be used to classify the sign of parameters such that the expected proportion of erroneous directional decisions (directional…
We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on…
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…
The local false discovery rate (lfdr) of Efron et al. (2001) enjoys major conceptual and decision-theoretic advantages over the false discovery rate (FDR) as an error criterion in multiple testing, but is only well-defined in Bayesian…
A new online multiple testing procedure is described in the context of anomaly detection, which controls the False Discovery Rate (FDR). An accurate anomaly detector must control the false positive rate at a prescribed level while keeping…
Consider a testing problem for the null hypothesis $H_0:\theta\in\Theta_0$. The standard frequentist practice is to reject the null hypothesis when the p-value is smaller than a threshold value $\alpha$, usually 0.05. We ask the question…
Consider the multiple testing problem of testing null hypotheses $H_1,...,H_s$. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($\mathit{FWER}$),…