Universality of sample covariance matrices: CLT of the smoothed empirical spectral distribution

2011/11/23 by Guangming Pan, Pan, Guangming, Qi-Man Shao +3
Computer Science · Mathematics · #15B52 #60F17 #62E20 #82B44 #Bayesian Methods and Mixture Models #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1111.5420

openalex publication_date 2011/11/23 · openalex created_date 2016/11/11 · openalex updated_date 2026/07/28

Abstract

A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.

Citations

• On the distribution of the largest eigenvalue in principal components analysis
• Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices
• On Estimation of a Probability Density Function and Mode

Related

• The universality principle for spectral distributions of sample covariance matrices
• A CLT for the LSS of large dimensional sample covariance matrices with unbounded dispersions
• Central limit theorem of nonparametric estimate of spectral density functions of sample covariance matrices
• CLT for LSS of sample covariance matrices with unbounded dispersions
• A Note on Central Limit Theorems for Linear Spectral Statistics of Large Dimensional F-matrix