Related papers: Sharp multiple testing boundary for sparse sequenc…
We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for $n$ independent, $p$-variate…
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…
We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic…
Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in \mathbb R^d$ and known covariance matrix $\Sigma = \operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal detection problem against sparse…
Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in…
Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
Multiple testing with false discovery rate (FDR) control has been widely conducted in the ``discrete paradigm" where p-values have discrete and heterogeneous null distributions. However, in this scenario existing FDR procedures often lose…
We investigate the multiplicity model with m values of some test statistic independently drawn from a mixture of no effect (null) and positive effect (alternative), where we seek to identify, the alternative test results with a controlled…
A new online multiple testing procedure is described in the context of anomaly detection, which controls the False Discovery Rate (FDR). An accurate anomaly detector must control the false positive rate at a prescribed level while keeping…
As the volume and complexity of data continue to expand across various scientific disciplines, the need for robust methods to account for the multiplicity of comparisons has grown widespread. A popular measure of type 1 error rate in…
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…
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…
The problem of simultaneously testing the marginal distributions of sequentially monitored, independent data streams is considered. The decisions for the various testing problems can be made at different times, using data from all streams,…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
We consider a matrix-valued Gaussian sequence model, that is, we observe a sequence of high-dimensional $M \times N$ matrices of heterogeneous Gaussian random variables $x_{ij,k}$ for $i \in\{1,...,M\}$, $j \in \{1,...,N\}$ and $k \in…
Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired…
We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…
We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at…
False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of "marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision…