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Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

Machine Learning · Statistics 2026-04-21 Antoine Chatalic , Marco Letizia , Nicolas Schreuder , Lorenzo Rosasco

An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…

Statistics Theory · Mathematics 2010-01-12 T. Tony Cai , Jiashun Jin

We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…

Statistics Theory · Mathematics 2020-02-11 T. Tony Cai , Hongji Wei

Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…

Statistics Theory · Mathematics 2026-05-13 Yikun Li , Matey Neykov

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

Machine Learning · Statistics 2014-06-24 Chao Ding , Hou-Duo Qi

We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…

Statistics Theory · Mathematics 2025-02-11 Per August Jarval Moen

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Optimization and Control · Mathematics 2026-05-07 Chandler Smith , HanQin Cai , Abiy Tasissa

We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…

Computational Geometry · Computer Science 2018-10-26 Ery Arias-Castro , Thibaut Le Gouic

We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…

Statistics Theory · Mathematics 2016-02-24 A. Goldenshluger , A. Juditski , A. Nemirovski

This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…

Information Theory · Computer Science 2020-05-15 Pierre Escamilla , Abdellatif Zaidi , Michèle Wigger

This note uses a simple example to show how moment inequality models used in the empirical economics literature lead to general minimax relative efficiency comparisons. The main point is that such models involve inference on a low…

Applications · Statistics 2014-12-19 Timothy B. Armstrong

We develop a novel computationally efficient and general framework for robust hypothesis testing. The new framework features a new way to construct uncertainty sets under the null and the alternative distributions, which are sets centered…

Machine Learning · Statistics 2018-05-29 Rui Gao , Liyan Xie , Yao Xie , Huan Xu

We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees…

Machine Learning · Statistics 2025-11-03 Binh Thuan Tran , Nicolas Schreuder

Correlation analysis is a fundamental step in uncovering meaningful insights from complex datasets. In this paper, we study the problem of detecting correlations between two random graphs following the Gaussian Wigner model with unlabeled…

Statistics Theory · Mathematics 2025-05-21 Dong Huang , Pengkun Yang

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

Statistics Theory · Mathematics 2015-03-06 Rajarshi Mukherjee , Natesh S. Pillai , Xihong Lin

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…

Machine Learning · Statistics 2016-01-27 Akshay Krishnamurthy

The aim of this paper is to establish non-asymptotic minimax rates of testing for goodness-of-fit hypotheses in a heteroscedastic setting. More precisely, we deal with sequences $(Y_j)_{j\in J}$ of independent Gaussian random variables,…

Statistics Theory · Mathematics 2010-02-09 Béatrice Laurent , Jean-Michel Loubès , Clément Marteau

We consider the problem of testing the hypothesis that the parameter of linear regression model is 0 against an s-sparse alternative separated from 0 in the l2-distance. We show that, in Gaussian linear regression model with p < n, where p…

Statistics Theory · Mathematics 2018-10-11 Alexandra Carpentier , Olivier Collier , Laëtitia Comminges , Alexandre B. Tsybakov , Yuhao Wang

We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…

Statistics Theory · Mathematics 2022-12-13 Botond Szabó , Lasse Vuursteen , Harry van Zanten

Upper and lower bounds are derived for the Gaussian mean width of the intersection of a convex hull of $M$ points with an Euclidean ball of a given radius. The upper bound holds for any collection of extreme point bounded in Euclidean norm.…

Statistics Theory · Mathematics 2017-09-28 Pierre C Bellec