A multivariate nonparametric test of independence Nail

By K. Bakirova, M. RIZZOb, Gábor J. Székelyc. 2006

A new nonparametric approach to the problem of testing the joint independence of two or more random vectors in arbitrary dimension is developed based on a measure of association determined by interpoint distances. The population independence coefficient takes values between 0 and 1, and equals zero if and only if the vectors are independent. We show that the corresponding statistic has a finite limit distribution if and only if the two random vectors are independent; thus we have a consistent test for independence. The coefficient is an increasing function of the absolute value of product moment correlation in the bivariate normal case, and coincides with the absolute value of correlation in the Bernoulli case. A simple modification of the statistic is affine invariant. The independence coefficient and the proposed statistic both have a natural extension to testing the independence of several random vectors. Empirical performance of the test is illustrated via a comparative Monte Carlo study. © 2005 Elsevier Inc. All rights reserved. AMS 1991 subject classification: Primary 62G10; secondary 62H20

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Citations in the corpus

Kernel‐based tests for joint independence (2016, methodology): “Bakirov et al. (2006) used an independence coefficient as the measure of dependence, which is defined as the normalized distance between the characteristic functions of the product and marginal distributions and is hence strongly related to the approach by Kankainen (1995).”
Strongly consistent nonparametric tests of conditional independence (2012, methodology): “As further literature we mention Bakirov et al. (2006), Beran et al. (2007), Dauxois and Nkiet (1998), Fukumizu et al. (2007), Gieser and Randles (1997), Gretton et al. (2005), Kankainen (1995), Genest et al.”