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The present paper establishes new multiple procedures for simultaneous testing of a large number of hypotheses under dependence. Special attention is devoted to experiments with rare false hypotheses. This sparsity assumption is typically…
In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of…
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…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
Machine learning applications frequently come with multiple diverse objectives and constraints that can change over time. Accordingly, trained models can be tuned with sets of hyper-parameters that affect their predictive behavior (e.g.,…
Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially…
A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations…
Multivariate statistics are often available as well as necessary in hypothesis tests. We study how to use such statistics to control not only false discovery rate (FDR) but also positive FDR (pFDR) with good power. We show that FDR can be…
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,…
Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false…
We consider the problem of asynchronous online testing, aimed at providing control of the false discovery rate (FDR) during a continual stream of data collection and testing, where each test may be a sequential test that can start and stop…
Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion. These problems, however, present unique challenges because of the subtle bias-and-variance tradeoff…
Adjustment of statistical significance levels for repeated analysis in group sequential trials has been understood for some time. Similarly, methods for adjustment accounting for testing multiple hypotheses are common. There is limited…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
Multiple hypothesis testing practices vary widely, without consensus on which are appropriate when. This paper provides an economic foundation for these practices designed to capture leading examples, such as regulatory approval on the…
This paper studies the means-testing problem under weakly correlated Normal setups. Although quite common in genomic applications, test procedures having exact FWER control under such dependence structures are nonexistent. We explore the…
Controlling the false discovery rate (FDR) in variable selection becomes challenging when predictors are correlated, as existing methods often exclude all members of correlated groups and consequently perform poorly for prediction. We…
We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model…
To identify statistically significant conclusions, it is proposed to simultaneously test hypotheses and alternatives. It is shown that, under the condition of free combination of hypotheses and alternatives, the closure method leads to…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…