The asymptotic variance matrix of the sample correlation matrix (Q753330)

Asymptotic distributions of sample covariance and sample correlation matrices are derived using the population-sample decomposition method [first published by \textit{B. M. S. van Praag}, \textit{J. de Leeuw} and \textit{T. Kloek}, Appl. Stochastic Models Data Anal. 2, 99-119 (1986; Zbl 0628.62052), and \textit{B. M. S. van Praag} and \textit{B. Wesselman}, Comput. Stat. Q. 1, 205-231 (1984; Zbl 0614.62078)]. The derivation uses the classic Lindeberg-Lévy central limit theorem and for this problem very well fitting notations and tools of matrix theory. The history of the problem is discussed, too.