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Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…

Methodology · Statistics 2014-04-29 Shurong Zheng , Z. D. Bai , Jiangfeng Yao

It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n$\in$Z with independent components satisfy at each…

Statistics Theory · Mathematics 2025-11-19 Philippe Loubaton , Alexis Rosuel , Pascal Vallet

In this paper, we establish the Central Limit Theorem (CLT) for linear spectral statistics (LSSs) of large-dimensional generalized spiked sample covariance matrices, where the spiked eigenvalues may be either bounded or diverge to infinity.…

Statistics Theory · Mathematics 2025-10-07 Zhijun Liu , Jiang Hu , Zhidong Bai , Zhihui Lv

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Logic in Computer Science · Computer Science 2026-03-10 Henning Basold , Oisín Flynn-Connolly , Chase Ford , Hao Wang

Let $\mathbf{X}_n=(x_{ij})$ be a $k \times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. We consider simultaneously $R$ sample covariance matrices…

Statistics Theory · Mathematics 2018-01-23 Weiming Li , Zeng Li , Jianfeng Yao

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

In this paper, we consider the empirical spectral distribution of the sample correlation matrix and investigate its asymptotic behavior under mild assumptions on the data's distribution, when dimension and sample size increase at the same…

Probability · Mathematics 2022-09-01 Nina Dörnemann , Johannes Heiny

This paper studies the central limit theorems (CLTs) for linear spectral statistics (LSSs) of general sample covariance matrices, when the test functions belong to $C^3$, the class of functions with continuous third order derivatives. We…

Statistics Theory · Mathematics 2026-03-16 Jian Cui , Zhijun Liu , Jiang Hu , Zhidong Bai

We study the central limit theorem (CLT) for linear eigenvalue statistics of several types of matrix models, whose entries are having exploding moments, i.e., moments of the entries are increasing with the size of the matrix. In particular,…

Probability · Mathematics 2026-04-30 Indrajit Jana , Sunita Rani

This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a…

Statistics Theory · Mathematics 2014-06-05 Damien Passemier , Matthew R. Mckay , Yang Chen

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked…

Statistics Theory · Mathematics 2015-06-18 Damien Passemier , Matthew R. Mckay , Yang Chen

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…

Statistics Theory · Mathematics 2023-12-25 Qianqian Jiang , Jiaxin Qiu , Zeng Li

Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…

Statistics Theory · Mathematics 2017-05-19 Weiming Li , Wang Zhou

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

Probability · Mathematics 2015-06-12 Florent Benaych-Georges , Alice Guionnet , Camille Male

In this paper, we investigate the spectral properties of the sample canonical correlation (SCC) matrix under the alternative hypothesis to provide a more comprehensive description of the association between two sets of variables. Our…

Statistics Theory · Mathematics 2023-09-26 Xiaozhuo Zhang

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…

Statistics Theory · Mathematics 2018-03-22 Jiang Hu , Weiming Li , Zhi Liu , Wang Zhou

In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population…

Statistics Theory · Mathematics 2021-04-09 Yanqing Yin

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

In this article, we first establish the joint central limit theorem (CLT) for the extreme eigenvalues of the sample correlation matrix of high-dimensional random walks with cross-sectional dependence. We further investigate the asymptotic…

Methodology · Statistics 2025-08-05 Ruihan Liu , Chen Wang

We consider two $n\times n$ non-Hermitian random matrices such that the $ij$th entry of one matrix is correlated with the $ij$th entry of the other matrix. However, the entries of any particular matrix are i.i.d. random variables. We study…

Probability · Mathematics 2025-04-08 Indrajit Jana , Sunita Rani