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Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…

Statistics Theory · Mathematics 2022-01-24 Yongcheng Qi , Yingchao Zhou

Pearson's Chi-squared test, though widely used for detecting association between categorical variables, exhibits low statistical power in large sparse contingency tables. To address this limitation, two novel permutation tests have been…

Methodology · Statistics 2024-03-27 Qingyang Zhang

The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…

Methodology · Statistics 2024-09-13 Mingshuo Liu , Doudou Zhou , Hao Chen

We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…

Methodology · Statistics 2025-08-18 Xuzhi Yang , Mona Azadkia , Tengyao Wang

Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…

Other Statistics · Statistics 2024-10-15 Xinbo Ai

Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…

Methodology · Statistics 2024-08-22 Yuwei Ke , Hok Kan Ling , Yanglei Song

We introduce a new test for conditional independence which is based on what we call the weighted generalised covariance measure (WGCM). It is an extension of the recently introduced generalised covariance measure (GCM). To test the null…

Methodology · Statistics 2022-05-17 Cyrill Scheidegger , Julia Hörrmann , Peter Bühlmann

The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…

Statistics Theory · Mathematics 2017-08-21 Luca Weihs , Mathias Drton , Nicolai Meinshausen

A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…

Machine Learning · Computer Science 2021-10-01 Silu Zhang , Xin Dang , Dao Nguyen , Dawn Wilkins , Yixin Chen

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

Methodology · Statistics 2026-01-28 Jinyuan Chang , Yue Du , Jing He , Qiwei Yao

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…

Statistics Theory · Mathematics 2019-11-15 Angshuman Roy , Anil Ghosh , Alok Goswami , C. A. Murthy

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any…

Machine Learning · Statistics 2024-06-27 Cencheng Shen , Sambit Panda , Joshua T. Vogelstein

Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…

Statistics Theory · Mathematics 2020-09-30 Fernando Castro-Prado , Wenceslao González-Manteiga

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…

Methodology · Statistics 2026-04-27 Bogdan Ćmiel , Teresa Ledwina

It is a common saying that testing for conditional independence, i.e., testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In…

Statistics Theory · Mathematics 2022-03-25 Rajen D. Shah , Jonas Peters

Re-sampling based statistical tests are known to be computationally heavy, but reliable when small sample sizes are available. Despite their nice theoretical properties not much effort has been put to make them efficient. In this paper we…

Methodology · Statistics 2018-06-29 Christina Chatzipantsiou , Marios Dimitriadis , Manos Papadakis , Michail Tsagris

We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…

Statistics Theory · Mathematics 2026-01-14 Mona Azadkia , Pouya Roudaki

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…

Statistics Theory · Mathematics 2008-12-18 Gábor J. Székely , Maria L. Rizzo , Nail K. Bakirov

Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…

Methodology · Statistics 2022-12-12 Siqi Liang , Faming Liang