Gaussian Fluctuations for Sample Covariance Matrices with Dependent Data

2012/03/20 by Olga Friesen, Matthias Löwe, Friesen, Olga +3
Mathematics · #60B20 #60F05 #Advanced Combinatorial Mathematics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics #math.PR #math.ST #msc:60B20 #msc:60F05 #stat.TH

paper · pdf · doi:10.48550/arxiv.1203.4387

28 pages

arxiv created 2012/03/20 · openalex publication_date 2012/03/20 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Marčenko-Pastur law remains unaffected if the rows and columns of Y_n exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of W_n also extends to the dependent case.

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