Multi-Panel Kendall plot in light of an ROC curve analysis applied to measuring dependence

Abstract

ABSTRACTThe Kendall plot (-plot) is a plot measuring dependence between the components of a bivariate random variable. The -plot graphs the Kendall distribution function against the distribution function of VU, where V and U are independent uniform random variables. We associate -plots with the receiver operating characteristic () curve, a well-accepted graphical tool in biostatistics for evaluating the ability of a biomarker to discriminate between two populations. The most commonly used global index of diagnostic accuracy of biomarkers is the area under the curve (). In parallel with the , we propose a novel strategy to measure association between random variables from a continuous bivariate distribution. First, we discuss why the area under the conventional Kendall curve () cannot be used as an index of dependence. We then suggest a simple and meaningful extension of the definition of the -plots, and define an index of dependence that is based on . This measure characterizes a wide range of two-variable relationships, thereby completely detecting the underlying dependence structure. Properties of the proposed index satisfy the mathematical definition of a measure. Finally, simulations and real data examples illustrate the applicability of the proposed method.