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The closure principle is fundamental in multiple testing and has been used to derive many efficient procedures with familywise error rate control. However, it is often unsuitable for modern research, which involves flexible multiple testing…

We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on…

Closed testing and partitioning are recognized as fundamental principles of familywise error control. In this paper, we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing. We…

In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…

We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER), extending to the…

The problem of multiple hypothesis testing arises when there are more than one hypothesis to be tested simultaneously for statistical significance. This is a very common situation in many data mining applications. For instance, assessing…

In complex clinical trials, multiple research objectives are often grouped into sets of objectives based on their inherent hierarchical relationships. Consequently, the hypotheses formulated to address these objectives are grouped into…

We describe a general framework for weighted parametric multiple test procedures based on the closure principle. We utilize general weighting strategies that can reflect complex study objectives and include many procedures in the literature…

Multiple hypothesis testing problems arise naturally in science. In this paper, we introduce the new Fast Closed Testing (FACT) method for multiple testing, controlling the family-wise error rate. This error rate is state of the art in many…

In clinical trials, hypotheses are frequently organized into hierarchically ordered families, requiring specialized testing strategies that account for these structured relationships. Existing gatekeeping methods-including serial, parallel,…

Large-scale multiple testing is a fundamental problem in high dimensional statistical inference. It is increasingly common that various types of auxiliary information, reflecting the structural relationship among the hypotheses, are…

Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…

In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…

In contemporary research, data scientists often test an infinite sequence of hypotheses $H_1,H_2,\ldots$ one by one, and are required to make real-time decisions without knowing the future hypotheses or data. In this paper, we consider such…

We consider a multiple hypothesis testing setting where the hypotheses are ordered and one is only permitted to reject an initial contiguous block, H_1,\dots,H_k, of hypotheses. A rejection rule in this setting amounts to a procedure for…

In this paper, we consider the problem of simultaneously testing many two-sided hypotheses when rejections of null hypotheses are accompanied by claims of the direction of the alternative. The fundamental goal is to construct methods that…

Conventional multiple hypothesis tests use step-up, step-down, or closed testing methods to control the overall error rates. We will discuss marrying these methods with adaptive multistage sampling rules and stopping rules to perform…

In many large multiple testing problems the hypotheses are divided into families. Given the data, families with evidence for true discoveries are selected, and hypotheses within them are tested. Neither controlling the error-rate in each…

Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…

A classical approach for dealing with the multiple testing problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of at least one false rejection. In many applications, one might be…