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We consider multiple testing means of many dependent Normal random variables that do not necessarily follow a joint Normal distribution. Under weak dependence, we show the uniform consistency of proportion estimators that are constructed as…
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…
This paper discusses several p-value-free multiple hypothesis testing methods proposed in recent years and organizes them by introducing a unified framework termed competition test. Although existing competition tests are effective in…
In multiple hypothesis testing, it is well known that adaptive procedures can enhance power via incorporating information about the number of true nulls present. Under independence, we establish that two adaptive false discovery rate (FDR)…
Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP),…
Many methods have been developed to estimate the set of relevant variables in a sparse linear model Y= XB+e where the dimension p of B can be much higher than the length n of Y. Here we propose two new methods based on multiple hypotheses…
In a one-way analysis-of-variance (ANOVA) model, the number of all pairwise comparisons can be large even when there are only a moderate number of groups. Motivated by this, we consider a regime with a growing number of groups, and prove…
The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative.…
We propose a new empirical Bayes method for covariate-assisted multiple testing with false discovery rate (FDR) control, where we model the local false discovery rate for each hypothesis as a function of both its covariates and p-value. Our…
Multiple tests are designed to test a whole collection of null hypotheses simultaneously. Their quality is often judged by the false discovery rate (FDR), i.e. the expectation of the quotient of the number of false rejections divided by the…
In this paper, we present novel methodologies that incorporate auxiliary variables for multiple hypotheses testing related to the main point of interest while effectively controlling the false discovery rate. When dealing with multiple…
We consider the problem of variable selection in high-dimensional statistical models where the goal is to report a set of variables, out of many predictors $X_1, \dotsc, X_p$, that are relevant to a response of interest. For linear…
MaxT is a highly popular resampling-based multiple testing procedure, which controls the Familywise Error Rate (FWER) and is powerful under dependence. This paper generalizes maxT to what we term ``multi-resolution'' False Discovery…
Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and…
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 this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…
Multiple testing literature contains ample research on controlling false discoveries for hypotheses classified according to one criterion, which we refer to as one-way classified hypotheses. Although simultaneous classification of…
In a multiple testing framework, we propose a method that identifies the interval with the highest estimated false discovery rate of P-values and rejects the corresponding null hypotheses. Unlike the Benjamini-Hochberg method, which does…
Large-scale hypothesis testing has become a ubiquitous problem in high-dimensional statistical inference, with broad applications in various scienfitic disciplines. One relevant application is constituted by imaging mass spectrometry (IMS)…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…