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When testing multiple hypotheses, a suitable error rate should be controlled even in exploratory trials. Conventional methods to control the False Discovery Rate (FDR) assume that all p-values are available at the time point of test…
Multiple hypothesis testing has been widely applied to problems dealing with high-dimensional data, e.g., selecting significant variables and controlling the selection error rate. The most prevailing measure of error rate used in the…
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding $p$-value) is known for each…
In the multiple testing problem with independent tests, the classical linear step-up procedure controls the false discovery rate (FDR) at level $\pi_0\alpha$, where $\pi_0$ is the proportion of true null hypotheses and $\alpha$ is the…
High-dimensional sparse generalized linear models (GLMs) have emerged in the setting that the number of samples and the dimension of variables are large, and even the dimension of variables grows faster than the number of samples. False…
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.…
The false discovery rate (FDR) and false nondiscovery rate (FNDR) have received considerable attention in the literature on multiple testing. These performance measures are also appropriate for classification, and in this work we develop…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
Conformal novelty detection is a classical machine learning task for which uncertainty quantification is essential for providing reliable results. Recent work has shown that the BH procedure applied to conformal p-values controls the false…
This paper studies the estimation of high dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the…
We provide new non-asymptotic false discovery proportion (FDP) confidence envelopes in several multiple testing settings relevant for modern high dimensional-data methods. We revisit the multiple testing scenarios considered in the recent…
The horseshoe prior, a widely used handy alternative to the spike-and-slab prior, has proven to be an exceptional default global-local shrinkage prior in Bayesian inference and machine learning. However, designing tests with frequentist…
Signal identification in large-dimensional settings is a challenging problem in biostatistics. Recently, the method of higher criticism (HC) was shown to be an effective means for determining appropriate decision thresholds. Here, we study…
Online testing procedures assume that hypotheses are observed in sequence, and allow the significance thresholds for upcoming tests to depend on the test statistics observed so far. Some of the most popular online methods include alpha…
We propose a novel multiple testing methodology for controlling the false discovery rate (FDR) in high-dimensional linear models that integrates model-X knockoff techniques with debiased penalized regression estimators. At the foundation of…
Simultaneously finding multiple influential variables and controlling the false discovery rate (FDR) for linear regression models is a fundamental problem. We here propose the Gaussian Mirror (GM) method, which creates for each predictor…
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…
Penalized regression methods are an attractive tool for high-dimensional data analysis, but their widespread adoption has been hampered by the difficulty of applying inferential tools. In particular, the question "How reliable is the…
We present a novel necessary and sufficient principle for False Discovery Rate (FDR) control. This e-Partitioning Principle says that a procedure controls FDR if and only if it is a special case of a general e-Partitioning procedure. By…
The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative.…