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We present a novel method for controlling the $k$-familywise error rate ($k$-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Cand\`es. Our procedure, which we also refer to as knockoffs,…
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…
This paper provides two general classes of multiple decision functions where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery…
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…
Some effort has been undertaken over the last decade to provide conditions for the control of the false discovery rate by the linear step-up procedure (LSU) for testing $n$ hypotheses when test statistics are dependent. In this paper we…
There is a growing interest in the implementation of platform trials, which provide the flexibility to incorporate new treatment arms during the trial and the ability to halt treatments early based on lack of benefit or observed…
When many (m) null hypotheses are tested with a single dataset, the control of the number of false rejections is often the principal consideration. Two popular controlling rates are the probability of making at least one false discovery…
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…
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…
The topic of multiple hypotheses testing now has a potpourri of novel theories and ubiquitous applications in diverse scientific fields. However, the universal utility of this field often hinders the possibility of having a generalized…
Platform trials offer a framework to study multiple interventions in a single trial with the opportunity of opening and closing arms. The use of a common control in platform trials can increase efficiency as compared to individual control…
Practical employment of Bayesian trial designs is still rare. Even if accepted in principle, the regulators have commonly required that such designs be calibrated according to an upper bound for the frequentist type I error rate. This…
In many scenarios such as genome-wide association studies where dependences between variables commonly exist, it is often of interest to infer the interaction effects in the model. However, testing pairwise interactions among millions of…
The False Discovery Rate (FDR) is a new statistical procedure to control the number of mistakes made when performing multiple hypothesis tests, i.e. when comparing many data against a given model hypothesis. The key advantage of FDR is that…
Modern biomedical research frequently involves testing multiple related hypotheses, while maintaining control over a suitable error rate. In many applications the false discovery rate (FDR), which is the expected proportion of false…
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…
We show that the control of the false discovery rate (FDR) for a multiple testing procedure is implied by two coupled simple sufficient conditions. The first one, which we call ``self-consistency condition'', concerns the algorithm itself,…
The $\gamma$-FDP and $k$-FWER multiple testing error metrics, which are tail probabilities of the respective error statistics, have become popular recently as less-stringent alternatives to the FDR and FWER. We propose general and flexible…
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.…
The family-wise error rate (FWER) has been widely used in genome-wide association studies. With the increasing availability of functional genomics data, it is possible to increase the detection power by leveraging these genomic functional…