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