相关论文: Elementary proofs of several results on false disc…
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…
Often in multiple testing, the hypotheses appear in non-overlapping blocks with the associated $p$-values exhibiting dependence within but not between blocks. We consider adapting the Benjamini-Hochberg method for controlling the false…
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…
Some crucial issues about a recently proposed estimator for the proportion of true null hypotheses ($\pi_0$) under discrete setup are discussed. An estimator for $\pi_0$ is introduced under the same setup. The estimator may be seen as a…
Consider the problem of simultaneously testing null hypotheses H_1,...,H_s. The usual approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of…
In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous…
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…
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…
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…
When testing a number of statistical hypotheses using data from location families, it is often useful to control the false discovery rate (FDR) not just for hypotheses of the null values but also of other parameter values that are deemed…
Consider the problem of testing multiple null hypotheses. A classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate ($FWER$), the probability of even one…
We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are…
When testing multiple hypothesis in a survey --e.g. many different source locations, template waveforms, and so on-- the final result consists in a set of confidence intervals, each one at a desired confidence level. But the probability…
We discuss several approaches to defining power in studies designed around the Benjamini-Hochberg (BH) false discovery rate (FDR) procedure. We focus primarily on the \textit{average power} and the $\lambda$-\textit{power}, which are the…
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…
Consider the problem of testing $s$ hypotheses simultaneously. The usual approach restricts attention to procedures that control the probability of even one false rejection, the familywise error rate (FWER). If $s$ is large, one might be…
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…
This analysis report presents an in-depth exploration of multiple hypothesis testing in the context of Genomics RNA-seq differential expression (DE) analysis, with a primary focus on techniques designed to control the false discovery rate…
We explicitly define the notions of (bona fide, approximate or asymptotic) compound p-values and e-values, which have been implicitly presented and used in the recent multiple testing literature. While it is known that the e-BH procedure…
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…