Related papers: On Benjamini-Hochberg procedure applied to mid p-v…

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…

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…

Considering the knockoff-based multiple testing framework of Barber and Cand\`es [2015], we revisit the method of Sarkar and Tang [2022] and identify it as a specific case of an un-normalized e-value weighted Benjamini-Hochberg procedure.…

There is recent interest in estimating the false discovery rate (FDR) with published p-values. However, there is little formal research that addresses the manner and extent to which the presumed selection, or publication, bias model impacts…

Large-scale multiple two-sample {\em Student}'s $t$ testing problems often arise from the statistical analysis of scientific data. To detect components with different values between two mean vectors, a well-known procedure is to apply the…

Conformal novelty detection is a classical machine learning task for which uncertainty quantification is essential for providing reliable results. Recent work has shown that the BH procedure applied to conformal p-values controls the false…

Multiple hypothesis testing is a core problem in statistical inference and arises in almost every scientific field. Given a set of null hypotheses $\mathcal{H}(n) = (H_1,\dotsc, H_n)$, Benjamini and Hochberg introduced the false discovery…

Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be…

In contemporary problems involving genetic or neuroimaging data, thousands of hypotheses need to be tested. Due to their high power, and finite sample guarantees on type-I error under weak assumptions, Monte Carlo permutation tests are…

The large bulk of work in multiple testing has focused on specifying procedures that control the false discovery rate (FDR), with relatively less attention being paid to the corresponding Type II error known as the false non-discovery rate…

One important partition of algorithms for controlling the false discovery rate (FDR) in multiple testing is into offline and online algorithms. The first generally achieve significantly higher power of discovery, while the latter allow…

In the context of multiple hypotheses testing, the proportion $\pi_0$ of true null hypotheses in the pool of hypotheses to test often plays a crucial role, although it is generally unknown a priori. A testing procedure using an implicit or…

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…

This paper extends the theory of false discovery rates (FDR) pioneered by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300]. We develop a framework in which the False Discovery Proportion (FDP)--the number of false…

Modern applications of conformal inference to multiple testing problems, such as outlier detection and candidate selection, often involve selecting test samples whose conformal p-values fall below a threshold. The quality of such methods is…

We address a common problem in large-scale data analysis, and especially the field of genetics, the huge-scale testing problem, where millions to billions of hypotheses are tested together creating a computational challenge to perform…

Multiple comparison procedures that control a family-wise error rate or false discovery rate provide an achieved error rate as the adjusted p-value for each hypothesis tested. However, since such p-values are not probabilities that the null…

In recent years, multiple hypothesis testing has come to the forefront of statistical research, ostensibly in relation to applications in genomics and some other emerging fields. The false discovery rate (FDR) and its variants provide very…

We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…

In many scenarios such as genome-wide association studies where dependences between variables commonly exist, it is often of interest to infer the interaction effects in the model. However, testing pairwise interactions among millions of…