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We propose a general and flexible procedure for testing multiple hypotheses about sequential (or streaming) data that simultaneously controls both the false discovery rate (FDR) and false nondiscovery rate (FNR) under minimal assumptions…
This paper is a review of the popular Benjamini Hochberg Method and other related useful methods of Multiple Hypothesis testing. This is written with the purpose of serving a short but complete easy to understand review of the main article…
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…
The introduction of the false discovery rate (FDR) by Benjamini and Hochberg has spurred a great interest in developing methodologies to control the FDR in various settings. The majority of existing approaches, however, address the FDR…
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…
Controlling the false discovery rate (FDR) is a powerful approach to multiple testing. In many applications, the tested hypotheses have an inherent hierarchical structure. In this paper, we focus on the fixed sequence structure where the…
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…
This paper develops a general framework for controlling the false discovery rate (FDR) in multiple testing of Gaussian means against two-sided alternatives. The widely used Benjamini-Hochberg (BH) procedure provides exact FDR control under…
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…
Complex large-scale studies, such as those related to microarray data and fMRI studies, often involve testing multiple hierarchically ordered hypotheses. However, most existing false discovery rate (FDR) controlling procedures do not…
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…
Improved procedures, in terms of smaller missed discovery rates (MDR), for performing multiple hypotheses testing with weak and strong control of the family-wise error rate (FWER) or the false discovery rate (FDR) are developed and studied.…
Much effort has been made to improve the famous step up test of Benjamini and Hochberg given by linear critical values $\frac{i\alpha}{n}$. It is pointed out by Gavrilov, Benjamini and Sarkar that step down multiple tests based on the…
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 multiple testing problems, where a large number of hypotheses are tested simultaneously, false discovery rate (FDR) control can be achieved with the well-known Benjamini-Hochberg procedure, which adapts to the amount of signal present in…
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.…
We investigate the performance of a family of multiple comparison procedures for strong control of the False Discovery Rate ($\mathsf{FDR}$). The $\mathsf{FDR}$ is the expected False Discovery Proportion ($\mathsf{FDP}$), that is, the…
A resurgence of interest in multiple hypothesis testing has occurred in the last decade. Motivated by studies in genomics, microarrays, DNA sequencing, drug screening, clinical trials, bioassays, education and psychology, statisticians have…
In hypothesis testing, a false discovery occurs when a hypothesis is incorrectly rejected due to noise in the sample. When adaptively testing multiple hypotheses, the probability of a false discovery increases as more tests are performed.…
We consider multiple testing with false discovery rate (FDR) control when p-values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less…