The asymptotic distributions of the largest entries of sample correlation matrices

Details The asymptotic distributions of the largest entries of sample correlation matrices The asymptotic distributions of the largest entries of sample correlation matrices

2004-06-09

arxiv.org/abs/math/0406184v1

Annals of Probability 2004, Vol. 14, No. 2, 865-880

Mathematics

Probability

Scientific paper

10.1214/105051604000000143

Let X_n=(x_{ij}) 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 R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry \rho_{ij} is the usual Pearson's correlation coefficient between the ith column of X_n and jth column of X_n. For contemporary data both n and p are large. When the population is a multivariate normal we study the test that H_0: the p variates of the population are uncorrelated. A test statistic is chosen as L_n=max_{i\ne j}|\rho_{ij}|. The asymptotic distribution of L_n is derived by using the Chen-Stein Poisson approximation method. Similar results for the non-Gaussian case are also derived.

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