Title: On convergence of the sample correlation matrices in high-dimensional data,
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.