Tests for assessing vector correlation

Article type: Research Article

Authors: El Maâche, Hamani | Lepage, Yves^{; *}

Affiliations: Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, QC, Canada H3C 3J7

Correspondence: [*] Corresponding author. E-mail: lepage@dms.UMontreal.ca.

Abstract: Three measures of multivariate relationship are revisited. These measures are used to construct nonparametric tests of the null hypothesis of independence of two sets of variables when the parent population distributions are unknown. Their asymptotic distributions are derived under the null hypothesis and under a sequence of alternatives from the asymptotic distribution of covariance and correlation matrices. The tests are illustrated by some examples and a simulation study is performed to compare the tests based on the covariance matrix with those based on the correlation matrix. We also compare these tests to other competitors based on Kendall's matrix and Spearman's matrix.

Keywords: U-statistics, asymptotic distribution, correlation matrix, measures of multivariate association, tests of independence

DOI: 10.3233/MAS-2007-2102

Journal: Model Assisted Statistics and Applications, vol. 2, no. 1, pp. 3-15, 2007