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The knockoff-based multiple testing setup of Barber & Candes (2015) for variable selection in multiple regression where sample size is as large as the number of explanatory variables is considered. The method of Benjamini & Hochberg (1995)…
The e-BH procedure is an e-value-based multiple testing procedure that provably controls the false discovery rate (FDR) under any dependence structure between the e-values. Despite this appealing theoretical FDR control guarantee, the e-BH…
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…
In high-throughput biology, it is common to fit thousands of linear regressions -- one per gene, protein, or other unit -- with very few samples per unit. Limma-trend, one of the most widely used methods in this setting, improves power by…
Controlling the False Discovery Rate (FDR) in a variable selection procedure is critical for reproducible discoveries, and it has been extensively studied in sparse linear models. However, it remains largely open in scenarios where the…
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…
Let $X_1,\ldots,X_n$ be a random sample from an unknown probability distribution $P$ on the sample space ${\cal X}$, and let $\theta=\theta(P)$ be a parameter of interest. The present paper proposes a nonparametric `Bayesian bootstrap'…
The topological gap protocol (TGP) is a statistical test designed to identify a topological phase with high confidence and without human bias. It is used to determine a promising parameter regime for operating topological qubits. The…
Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…
Let $X_{1},\ldots,X_{n}$ be i.i.d. sample in $\mathbb{R}^{p}$ with zero mean and the covariance matrix $\mathbf{\Sigma}$. The problem of recovering the projector onto an eigenspace of $\mathbf{\Sigma}$ from these observations naturally…
When conducting large scale inference, such as genome-wide association studies or image analysis, nominal $p$-values are often adjusted to improve control over the family-wise error rate (FWER). When the majority of tests are null,…
Recent advances in molecular simulations allow the evaluation of previously unattainable observables, such as rate constants for protein folding. However, these calculations are usually computationally expensive and even significant…
Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $\hat\Sigma$ denote the sample…
The false discovery proportion (FDP) is a convenient way to account for false positives when a large number $m$ of tests are performed simultaneously. Romano and Wolf [Ann. Statist. 35 (2007) 1378-1408] have proposed a general principle…
This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Modern data analysis frequently involves large-scale hypothesis testing, which naturally gives rise to the problem of maintaining control of a suitable type I error rate, such as the false discovery rate (FDR). In many biomedical and…
We consider the problem of variable selection in high-dimensional statistical models where the goal is to report a set of variables, out of many predictors $X_1, \dotsc, X_p$, that are relevant to a response of interest. For linear…
While data-driven confounder selection requires careful consideration, it is frequently employed in observational studies. Widely recognized criteria for confounder selection include the minimal-set approach, which involves selecting…
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.…