Tests of Multivariate Independence for Ordinal Data

Abstract

Population and sample versions of Kendall and Spearman measures of association suitable for multivariate ordinal data are defined. The latter generalize the indices of dependence of Ruymgaart and van Zuijlen (1978), Joe (1990), and Schmid and Schmidt (2007) by allowing atoms in the underlying distribution. The representation of the proposed empirical measures as U-statistics enables to establish their asymptotic normality under general distributions. A special attention is given to tests of independence for multivariate ordinal data, where the power of the new methodologies are investigated under fixed and contiguous alternatives.

Keywords:

• Contiguous alternatives
• Copula-based discrete models
• Kendall's tau
• Multivariate Poisson distribution
• Ordinal data
• Spearman's rho

Mathematics Subject Classification:

• Primary 62H20
• Secondary 62G10

Acknowledgments

A referee is gratefully acknowledged for comments and suggestions that improved the quality of the article. Funding in partial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada.