Nonlinear rank correlations

Rank correlation is a fundamental tool to express dependence in cases in which the data are arranged in order. There are, by contrast, circumstances where the ordinal association is of a nonlinear type. In this paper we investigate the eectiveness of several coecients of rank correlation. These measures have been divided into three classes: conventional rank correlations, weighted rank correlations, correlations of scores. Our ndings suggest that none is systematically better than the other in all circumstances. However, a simply weighted version of the Kendall's provides plausible answers to many special situations where intercategory distances could not be considered on the same basis.