Related papers: Combining independent p-values in replicability an…
In the setting of multiple testing, compound p-values generalize p-values by asking for superuniformity to hold only \emph{on average} across all true nulls. We study the properties of the Benjamini--Hochberg procedure applied to compound…
Good's formula and Fisher's method are frequently used for combining independent P-values. Interestingly, the equivalent of Good's formula already emerged in 1910 and mathematical expressions relevant to even more general situations have…
We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $\epsilon$ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary…
In the context of large-scale multiple testing, hypotheses are often accompanied with certain prior information. In this paper, we present a single-index modulated (SIM) multiple testing procedure, which maintains control of the false…
Replicability is a lynchpin for credible discoveries. The partial conjunction (PC) p-value, which combines individual base p-values from multiple similar studies, can gauge whether a feature of interest exhibits replicated signals across…
Combining dependent p-values poses a long-standing challenge in statistical inference, particularly when aggregating findings from multiple methods to enhance signal detection. Recently, p-value combination tests based on regularly…
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling…
The two-trials rule in drug regulation requires statistically significant results from two pivotal trials to demonstrate efficacy. However, it is unclear how the effect estimates from both trials should be combined to quantify the drug…
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…
In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on the number of false discoveries in the selected set. Many…
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…
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…
A novel class of methods for combining $p$-values to perform aggregate hypothesis tests has emerged that exploit the properties of heavy-tailed Stable distributions. These methods offer important practical advantages including robustness to…
Replicability analysis aims to identify the findings that replicated across independent studies that examine the same features. We provide powerful novel replicability analysis procedures for two studies for FWER and for FDR control on the…
We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means or medians of the random variables belonging to a non-empty, bounded interval; (ii) the means or medians of the random…
Verifying that a statistically significant result is scientifically meaningful is not only good scientific practice, it is a natural way to control the Type I error rate. Here we introduce a novel extension of the p-value - a…
The following zero-sum game between nature and a statistician blends Bayesian methods with frequentist methods such as p-values and confidence intervals. Nature chooses a posterior distribution consistent with a set of possible priors. At…
Microarray analysis to monitor expression activities in thousands of genes simultaneously has become routine in biomedical research during the past decade. A tremendous amount of expression profiles are generated and stored in the public…
We study a statistical framework for replicability based on a recently proposed quantitative measure of replication success, the sceptical $p$-value. A recalibration is proposed to obtain exact overall Type-I error control if the effect is…
In this paper we use e-values in the context of multiple hypothesis testing assuming that the base tests produce independent, or sequential, e-values. Our simulation and empirical studies and theoretical considerations suggest that, under…