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May 2004 The asymptotic distributions of the largest entries of sample correlation matrices
Tiefeng Jiang
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Ann. Appl. Probab. 14(2): 865-880 (May 2004). DOI: 10.1214/105051604000000143


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 ijij|. 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.


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Tiefeng Jiang. "The asymptotic distributions of the largest entries of sample correlation matrices." Ann. Appl. Probab. 14 (2) 865 - 880, May 2004.


Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1047.60014
MathSciNet: MR2052906
Digital Object Identifier: 10.1214/105051604000000143

Primary: 60F05 , 60F15 , 62H10

Keywords: Chen–Stein method , Maxima , Moderate deviations , Sample correlation matrices

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 2 • May 2004
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