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Large-scale simultaneous hypothesis testing appears in many areas such as microarray studies, genome-wide association studies, brain imaging, disease mapping and astronomical surveys. A well-known inference method is to control the false…
Familywise error rate (FWER) has been a cornerstone in simultaneous inference for decades, and the classical Bonferroni method has been one of the most prominent frequentist approaches for controlling FWER. The present article studies the…
Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost:…
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 consider the problem of multiple hypothesis testing with generic side information: for each hypothesis $H_i$ we observe both a p-value $p_i$ and some predictor $x_i$ encoding contextual information about the hypothesis. For large-scale…
It is frequently of interest to jointly analyze multiple sequences of multiple tests in order to identify simultaneous signals, defined as features tested in multiple studies whose test statistics are non-null in each. In many problems,…
The standard paradigm for confirmatory clinical trials is to compare experimental treatments with a control, for example the standard of care or a placebo. However, it is not always the case that a suitable control exists. Efficient…
Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an…
This paper revisits the following open question in simultaneous testing of multivariate normal means against two-sided alternatives: Can the method of Benjamini and Hochberg (BH, 1995) control the false discovery rate (FDR) without imposing…
A cornerstone of the multiple testing literature is the Benjamini-Hochberg (BH) procedure, which guarantees control of the FDR when $p$-values are independent or positively dependent. While BH controls the average quality of rejections, it…
We study asymptotic properties of Bayesian multiple testing procedures and provide sufficient conditions for strong consistency under general dependence structure. We also consider a novel Bayesian multiple testing procedure and associated…
Many modern applications require using data to select the statistical tasks and make valid inference after selection. In this article, we provide a unifying approach to control for a class of selective risks. Our method is motivated by a…
How to weigh the Benjamini-Hochberg procedure? In the context of multiple hypothesis testing, we propose a new step-wise procedure that controls the false discovery rate (FDR) and we prove it to be more powerful than any weighted…
Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
We provide an approach to exploratory data analysis in matched observational studies with a single intervention and multiple endpoints. In such settings, the researcher would like to explore evidence for actual treatment effects among these…
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…
We introduce a multiple testing procedure that controls the median of the proportion of false discoveries (FDP) in a flexible way. The procedure only requires a vector of p-values as input and is comparable to the Benjamini-Hochberg method,…
While traditional multiple testing procedures prohibit adaptive analysis choices made by users, Goeman and Solari (2011) proposed a simultaneous inference framework that allows users such flexibility while preserving high-probability bounds…