Related papers: A central limit theorem for the Benjamini-Hochberg…
We investigate the multiplicity model with m values of some test statistic independently drawn from a mixture of no effect (null) and positive effect (alternative), where we seek to identify, the alternative test results with a controlled…
E-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. In brief, e-values are realized by random variables with expectation at most one under the null; examples include…
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…
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…
Multiple testing adjustments, such as the Benjamini and Hochberg (1995) step-up procedure for controlling the false discovery rate (FDR), are typically applied to families of tests that control significance level in the classical sense: for…
Multiple testing has been a popular topic in statistical research. Although vast works have been done, controlling the false discoveries remains a challenging task when the corresponding test statistics are dependent. Various methods have…
False discovery rate (FDR) is a commonly used criterion in multiple testing and the Benjamini-Hochberg (BH) procedure is arguably the most popular approach with FDR guarantee. To improve power, the adaptive BH procedure has been proposed by…
In multiple testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini-Hochberg procedure, which adapts to the amount of signal present in…
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…
False discovery rate (FDR) has been a key metric for error control in multiple hypothesis testing, and many methods have developed for FDR control across a diverse cross-section of settings and applications. We develop a closure principle…
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…
We consider the problem of comparing a reference distribution with several other distributions. Given a sample from both the reference and the comparison groups, we aim to identify the comparison groups whose distributions differ from that…
We propose sufficient conditions and computationally efficient procedures for false discovery rate control in multiple testing when the $p$-values are related by a known \emph{dependency graph} -- meaning that we assume independence of…
Multiple hypotheses testing is a core problem in statistical inference and arises in almost every scientific field. Given a sequence of null hypotheses $\mathcal{H}(n) = (H_1,..., H_n)$, Benjamini and Hochberg…
This paper introduces the \texttt{FDR-linking} theorem, a novel technique for understanding \textit{non-asymptotic} FDR control of the Benjamini--Hochberg (BH) procedure under arbitrary dependence of the $p$-values. This theorem offers a…
We propose a novel multiple testing methodology for controlling the false discovery rate (FDR) in high-dimensional linear models that integrates model-X knockoff techniques with debiased penalized regression estimators. At the foundation of…
Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the family-wise error rate in multiple testing problems, and proposed a procedure to control the FDR. For discrete data this procedure may be highly…
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.…
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…
When testing many hypotheses, often we do not have strong expectations about the directions of the effects. In some situations however, the alternative hypotheses are that the parameters lie in a certain direction or interval, and it is in…