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On convergence of the sample correlation matrices in high-dimensional data

2017/06/20 by Sévérien Nkurunziza, Nkurunziza, Sévérien, Yueleng Wang +1
Decision Sciences · Mathematics · #FOS: Mathematics #Probability and Risk Models #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1706.06638

openalex publication_date 2017/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider an estimation problem concerning the matrix of correlation coefficients in context of high dimensional data settings. In particular, we revisit some results in Li and Rolsalsky [Li, D. and Rolsalsky, A. (2006). Some strong limit theorems for the largest entries of sample correlation matrices, The Annals of Applied Probability, 16, 1, 423-447]. Four of the main theorems of Li and Rolsalsky (2006) are established in their full generalities and we simplify substantially some proofs of the quoted paper. Further, we generalize a theorem which is useful in deriving the existence of the pth moment as well as in studying the convergence rates in law of large numbers.

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