The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 2 (2004), 865-880.
The asymptotic distributions of the largest entries of sample correlation matrices
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.
Ann. Appl. Probab., Volume 14, Number 2 (2004), 865-880.
First available in Project Euclid: 23 April 2004
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Jiang, Tiefeng. The asymptotic distributions of the largest entries of sample correlation matrices. Ann. Appl. Probab. 14 (2004), no. 2, 865--880. doi:10.1214/105051604000000143. https://projecteuclid.org/euclid.aoap/1082737115