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
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.