An exchangeable Kendall's tau for clustered data

Abstract

Abstract This article introduces the exchangeable Kendall's tau as a nonparametric intraclass association measure in a clustered data frame and studies the sampling properties of an estimator of this quantity. Its asymptotic distribution is derived under a multivariate exchangeable model. Two applications of the proposed statistic are considered. The first is an estimator of the intraclass correlation coefficient for data drawn from an elliptical distribution. The asymptotic properties of this estimator are investigated under an extended random effects ANOVA model. The second is a semiparametric intraclass independence test based on the exchangeable Kendall's tau whose performance is assessed using Pitman efficiencies and a Monte Carlo study. The Canadian Journal of Statistics 42: 384–403; 2014 © 2014 Statistical Society of Canada