Central Limit Theorem for Linear Eigenvalue Statistics for a Tensor Product Version of Sample Covariance Matrices

Journal of Theoretical Probability ◽

10.1007/s10959-017-0741-9 ◽

2017 ◽

Vol 31 (2) ◽

pp. 1024-1057 ◽

Cited By ~ 5

Author(s):

A. Lytova

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Tensor Product ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Linear Eigenvalue Statistics ◽

Sample Covariance ◽

Eigenvalue Statistics

Download Full-text

On Asymptotic Expansion and Central Limit Theorem of Linear Eigenvalue Statistics for Sample Covariance Matrices when ${N/M\rightarrow0}$

Theory of Probability and Its Applications ◽

10.1137/s0040585x97t987089 ◽

2015 ◽

Vol 59 (2) ◽

pp. 185-207

Author(s):

Z. Bao

Keyword(s):

Asymptotic Expansion ◽

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Linear Eigenvalue Statistics ◽

Sample Covariance ◽

Eigenvalue Statistics

Download Full-text

Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrices and sample covariance matrices

Annales de l Institut Henri Poincaré Probabilités et Statistiques ◽

10.1214/20-aihp1086 ◽

2021 ◽

Vol 57 (1) ◽

Author(s):

Yiting Li ◽

Kevin Schnelli ◽

Yuanyuan Xu

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Wigner Matrices ◽

Sample Covariance ◽

Eigenvalue Statistics

Download Full-text

Joint Central Limit Theorem for Eigenvalue Statistics from Several Dependent Large Dimensional Sample Covariance Matrices with Application

Scandinavian Journal of Statistics ◽

10.1111/sjos.12320 ◽

2018 ◽

Vol 45 (3) ◽

pp. 699-728 ◽

Cited By ~ 2

Author(s):

Weiming Li ◽

Zeng Li ◽

Jianfeng Yao

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Eigenvalue Statistics

Download Full-text

Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices

Bernoulli ◽

10.3150/18-bej1038 ◽

2019 ◽

Vol 25 (3) ◽

pp. 1838-1869 ◽

Cited By ~ 1

Author(s):

Zhidong Bai ◽

Huiqin Li ◽

Guangming Pan

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Spectral Statistics

Download Full-text

Central limit theorem for linear spectral statistics of large dimensional quaternion sample covariance matrices

Linear Algebra and its Applications ◽

10.1016/j.laa.2018.05.031 ◽

2018 ◽

Vol 554 ◽

pp. 275-315

Author(s):

Yanqing Yin

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Spectral Statistics

Download Full-text

Central limit theorem for the spiked eigenvalues of separable sample covariance matrices

10.32657/10356/70338 ◽

2017 ◽

Author(s):

◽

Bo Zhang

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Sample Covariance

Download Full-text

Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2020.06.003 ◽

2021 ◽

Vol 211 ◽

pp. 80-89

Author(s):

Huiqin Li ◽

Yanqing Yin ◽

Shurong Zheng

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Covariance Matrices ◽

Sample Covariance Matrices ◽

Sample Covariance ◽

Spectral Statistics

Download Full-text

Central limit theorem for linear eigenvalue statistics of the Wigner and the sample covariance random matrices

Metrika ◽

10.1007/s00184-008-0212-5 ◽

2008 ◽

Vol 69 (2-3) ◽

pp. 153-172 ◽

Cited By ~ 4

Author(s):

Anna Lytova ◽

Leonid Pastur

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Random Matrices ◽

Central Limit ◽

Linear Eigenvalue Statistics ◽

Sample Covariance ◽

Eigenvalue Statistics

Download Full-text

Gaussian ensembles: Central Limit Theorem for linear eigenvalue statistics

Eigenvalue Distribution of Large Random Matrices - Mathematical Surveys and Monographs ◽

10.1090/surv/171/03 ◽

2011 ◽

pp. 69-100

Author(s):

Leonid Pastur ◽

Mariya Shcherbina

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Central Limit ◽

Linear Eigenvalue Statistics ◽

Eigenvalue Statistics ◽

Gaussian Ensembles

Download Full-text

On the fluctuations of eigenvalues of multiplicative deformed unitary invariant ensembles

Random Matrices Theory and Application ◽

10.1142/s2010326316500076 ◽

2016 ◽

Vol 05 (02) ◽

pp. 1650007 ◽

Cited By ~ 1

Author(s):

Vladimir Vasilchuk

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Random Matrices ◽

Central Limit ◽

Counting Measure ◽

Linear Eigenvalue Statistics ◽

The Central Limit Theorem ◽

Eigenvalue Statistics ◽

Leading Term

We consider the ensemble of [Formula: see text] random matrices [Formula: see text], where [Formula: see text] and [Formula: see text] are non-random, unitary, having the limiting Normalized Counting Measure (NCM) of eigenvalues, and [Formula: see text] is unitary, uniformly distributed over [Formula: see text]. We find the leading term of the covariance of traces of resolvent of [Formula: see text] and establish the Central Limit Theorem for sufficiently smooth linear eigenvalue statistics of [Formula: see text] as [Formula: see text].

Download Full-text