The asymptotic distributions of the largest entries of sample correlation matrices

The asymptotic distributions of the largest entries of sample correlation matrices

Tiefeng Jiang

Source: Ann. Appl. Probab. Volume 14, Number 2 (2004), 865-880.

Abstract

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=(ρ_ij) be the p×p sample correlation matrix of X_n; that is, the entry ρ_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 H₀: the p variates of the population are uncorrelated. A test statistic is chosen as L_n=max _i≠j|ρ_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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Primary Subjects: 60F05, 60F15, 62H10

Keywords: Sample correlation matrices; maxima; Chen–Stein method; moderate deviations

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737115
Digital Object Identifier: doi:10.1214/105051604000000143
Mathematical Reviews number (MathSciNet): MR2052906
Zentralblatt MATH identifier: 1047.60014

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