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We establish a Cram\'er-type moderate deviation result for self-normalized sums of weakly dependent random variables, where the moment requirement is much weaker than the non-self-normalized counterpart. The range of the moderate deviation…

Statistics Theory · Mathematics 2014-09-15 Xiaohong Chen , Qi-Man Shao , Wei Biao Wu

By studying the family of $p$-dimensional scale mixtures, this paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix {\em does not converge} to the celebrated…

Methodology · Statistics 2017-05-16 Weiming Li , Jianfeng Yao

We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…

Methodology · Statistics 2022-05-16 Jiří Dvořák , Tomáš Mrkvička

This paper establishes the asymptotic independence between the quadratic form and maximum of a sequence of independent random variables. Based on this theoretical result, we find the asymptotic joint distribution for the quadratic form and…

Methodology · Statistics 2023-08-03 Dachuan Chen , Decai Liang , Long Feng

This article addresses the problem of testing the conditional independence of two generic random vectors $X$ and $Y$ given a third random vector $Z$, which plays an important role in statistical and machine learning applications. We propose…

Methodology · Statistics 2024-07-26 Yi Zhang , Linjun Huang , Yun Yang , Xiaofeng Shao

The categorical Gini correlation proposed by Dang et al. is a dependence measure to characterize independence between categorical and numerical variables. The asymptotic distributions of the sample correlation under dependence and…

Statistics Theory · Mathematics 2023-04-19 Yongli Sang , Xin Dang

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…

Information Theory · Computer Science 2022-11-08 Anand Jerry George , Clément L. Canonne

This paper aims to test the number of spikes in a generalized spiked covariance matrix, the spiked eigenvalues of which may be extremely larger or smaller than the non-spiked ones. For a high-dimensional problem, we first propose a general…

Methodology · Statistics 2022-03-15 Dandan Jiang

Two parties observe independent copies of a $d$-dimensional vector and a scalar. They seek to test if their data is correlated or not, namely they seek to test if the norm $\|\rho\|_2$ of the correlation vector $\rho$ between their…

Information Theory · Computer Science 2020-05-22 K. R. Sahasranand , Himanshu Tyagi

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…

Statistics Theory · Mathematics 2013-10-31 Rongmao Zhang , Liang Peng , Ruodu Wang

We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…

Probability · Mathematics 2009-12-11 Noureddine El Karoui

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…

Methodology · Statistics 2019-04-16 Ćmiel Bogdan , Ledwina Teresa

This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…

Methodology · Statistics 2025-12-01 Yuchen Hu , Xiaoyi Wang , Long Feng

High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample…

Statistics Theory · Mathematics 2024-05-14 Daning Bi , Xiao Han , Adam Nie , Yanrong Yang

This paper proposes a new test for covariance matrices structure based on the correction to Rao's score test in large dimensional framework. By generalizing the CLT for the linear spectral statistics of large dimensional sample covariance…

Methodology · Statistics 2015-12-22 Dandan Jiang

We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…

Disordered Systems and Neural Networks · Physics 2026-05-21 Yaprak Önder , Abbas Ali Saberi , Roderich Moessner

This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using…

Information Theory · Computer Science 2016-11-18 Romain Couillet , Frederic Pascal , Jack W. Silverstein

We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…

Statistics Theory · Mathematics 2024-04-19 Nour-Eddine Berrahou , Salim Bouzebda , Lahcen Douge

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

Statistics Theory · Mathematics 2024-02-14 Patrick Bastian , Holger Dette , Johannes Heiny

We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between…

Methodology · Statistics 2026-05-22 Muyi Li , Yuqing Xu , Zhou Zhou