2004/06/09 by Tiefeng Jiang · 1 citation
Mathematics · #math.PR #msc:60F05 #msc:60F15 #msc:62H10
paper · pdf · doi:10.1214/105051604000000143
published as Annals of Probability 2004, Vol. 14, No. 2, 865-880
arxiv created 2004/06/09 · arxiv updated 2009/12/01
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=maxi≠ 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.