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This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

Statistics Theory · Mathematics 2020-06-01 Rémy Mariétan , Stephan Morgenthaler

For testing the independence of two vectors with respective dimensions $p_1$ and $p_2$, the existing literature in high-dimensional statistics all assume that both dimensions $p_1$ and $p_2$ grow to infinity with the sample size. However,…

Methodology · Statistics 2018-01-23 Weiming Li , Jiaqi Chen , Jianfeng Yao

We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…

Statistics Theory · Mathematics 2016-12-05 Dennis Leung , Mathias Drton

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…

Machine Learning · Statistics 2026-03-23 Nathaniel Xu , Feng Liu , Danica J. Sutherland

This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…

Statistics Theory · Mathematics 2025-09-16 Bilol Banerjee

Relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Many statistical methods for the analysis of such data assume some degree of similarity or dependence between…

Statistics Theory · Mathematics 2013-06-26 Alexander Volfovsky , Peter D. Hoff

In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…

Methodology · Statistics 2017-09-20 Shun Yao , Xianyang Zhang , Xiaofeng Shao

This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the…

Statistics Theory · Mathematics 2025-10-09 Zhaorui Dong , Fang Han , Jianfeng Yao

In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…

Methodology · Statistics 2015-03-24 Kazuyoshi Yata , Makoto Aoshima

In this article, we consider the complete independence test of high-dimensional data. Based on Chatterjee coefficient, we pioneer the development of quadratic test and extreme value test which possess good testing performance for…

Statistics Theory · Mathematics 2024-09-17 Liqi Xia , Ruiyuan Cao , Jiang Du , Jun Dai

Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…

Methodology · Statistics 2014-08-19 Julie Josse , Susan Holmes

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

Statistics Theory · Mathematics 2019-12-17 Xinxin Yang , Xinghua Zheng , Jiaqi Chen

This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…

Statistics Theory · Mathematics 2020-03-09 Rémy Mariétan , Stephan Morgenthaler

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

Statistics Theory · Mathematics 2020-09-25 Zhixiang Zhang , Shurong Zheng , Guangming Pan , Pingshou Zhong

We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…

Statistics Theory · Mathematics 2025-11-19 Holger Dette , Marius Kroll

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

Methodology · Statistics 2023-06-13 Zhanrui Cai , Jing Lei , Kathryn Roeder

We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…

Statistics Theory · Mathematics 2022-11-11 Terence Kevin Manfoumbi Djonguet , Guy Martial Nkiet

We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…

Statistics Theory · Mathematics 2025-10-03 Siegfried Hörmann , Daniel Strenger-Galvis

In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…

Statistics Theory · Mathematics 2024-10-15 Suprio Bhar , Subhra Sankar Dhar

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting non-linear, non-monotone relationships,…

Statistics Theory · Mathematics 2020-02-06 Mathias Drton , Fang Han , Hongjian Shi