Let Xn=(xij) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let Rn=(ρij) be the p×p sample correlation matrix of Xn; that is, the entry ρij is the usual Pearson”s correlation coefficient between the ith column of Xn and jth column of Xn. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H0: the p variates of the population are uncorrelated. A test statistic is chosen as Ln=max i≠j|ρij|. The asymptotic distribution of Ln is derived by using the Chen–Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived.
@article{1082737115,
author = {Jiang, Tiefeng},
title = {The asymptotic distributions of the largest entries of sample correlation matrices},
journal = {Ann. Appl. Probab.},
volume = {14},
number = {1},
year = {2004},
pages = { 865-880},
language = {en},
url = {http://dml.mathdoc.fr/item/1082737115}
}
Jiang, Tiefeng. The asymptotic distributions of the largest entries of sample correlation matrices. Ann. Appl. Probab., Tome 14 (2004) no. 1, pp. 865-880. http://gdmltest.u-ga.fr/item/1082737115/