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We propose a general scheme to create time sequences that fulfill given constraints but are random otherwise. Significance levels for nonlinearity tests are as usually obtained by Monte Carlo resampling. In a new scheme, constraints…
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…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
Simultaneously testing $K$ hypotheses while controlling the family-wise error rate is a fundamental problem in statistics. Existing procedures (Bonferroni, Holm, Hochberg, Hommel) provide valid control but sacrifice power, increasingly so…
Identifying the most powerful test in multiple hypothesis testing under strong family-wise error rate (FWER) control is a fundamental problem in statistical methodology. State-of-the-art approaches formulate this as a constrained…
In this paper, we deal with sequential testing of multiple hypotheses. In the general scheme of construction of optimal tests based on the backward induction, we propose a modification which provides a simplified (generally speaking,…
While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this…
Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ at this stage can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we…
Online testing procedures aim to control the extent of false discoveries over a sequence of hypothesis tests, allowing for the possibility that early-stage test results influence the choice of hypotheses to be tested in later stages.…
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:…
Crossover designs are an extremely useful tool to investigators, whilst group sequential methods have proven highly proficient at improving the efficiency of parallel group trials. Yet, group sequential methods and crossover designs have…
When hypotheses are tested in a stream and real-time decision-making is needed, online sequential hypothesis testing procedures are needed. Furthermore, these hypotheses are commonly partitioned into groups by their nature. For example, the…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
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…
In a multiple testing problem where one is willing to tolerate a few false rejections, procedure controlling the familywise error rate (FWER) can potentially be improved in terms of its ability to detect false null hypotheses by…
We consider the problem of sequential multiple hypothesis testing with nontrivial data collection costs. This problem appears, for example, when conducting biological experiments to identify differentially expressed genes of a disease…
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to…
The standard paired-sample testing approach in the multidimensional setting applies multiple univariate tests on the individual features, followed by p-value adjustments. Such an approach suffers when the data carry numerous features. A…
Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the…
This paper presents a survey on some recent advances for the type I error rate control in multiple testing methodology. We consider the problem of controlling the $k$-family-wise error rate (kFWER, probability to make $k$ false discoveries…