H. Neudecker, THE ASYMPTOTIC VARIANCE MATRICES OF THE SAMPLE CORRELATION MATRIX IN ELLIPTIC AND NORMAL SITUATIONS AND THEIR PROPORTIONALITY, Linear algebra and its applications, 237, 1996, pp. 127-132
This note presents the asymptotic variance matrices of the sample corr
elation matrix in elliptical and normal situations and generalizes the
scalar proportionality result to the multivariate case.