EXPLORING KENDALL'S TAU AND ITS RELATION TO COPULA - Octavina
One of measure of association between two continuous random variables, used widely for monotonically linear or non-linear cases, is Kendall's Tau. We explore the pro- perties of Kendall's Tau according to the concept of concordance. First of all, we dene a monotonic and bijective function, named rank, to generalize concordant and discordant denitions. Then, we employ such generalization to derive the unique- ness of both concordant and discordant pairs proportion for each Kendall's Tau coecient. The relation between Kendall's tau and Copula is also investigated. In particu- lar, we provide extensive derivation on invariance property under non-linear strictly increasing transformation for Kendall's Tau as well as Copula representation for Kendall's Tau. We nd that Copula parameter leads to the strength of association. Furthermore, the behavior of bivariate observations may be explained descriptively through Copula.