Detecting Dependence With Kendall Plots

Abstract

Earlier literature proposed a rank-based graphical tool called a chi-plot which, in conjunction with a traditional scatterplot of the raw data, can help detect the presence of association in a random sample from some continuous bivariate distribution. This article suggests an alternative display called a Kendall plot, or K-plot for short, which adapts the concept of probability plot to the detection of dependence. The new procedure, which is rooted in the probability integral transformation, retains the chi-plot's key property of invariance with respect to monotone transformations of the marginal distributions. K-plots are easier to interpret than chi-plots, however, because the curvature that they display in cases of association is related in a definite way to the copula characterizing the underlying dependence structure. In addition, K-plots have the advantage of being readily extendible to the multivariate context.