The use of nonnull models for ranks in nonparametric statistics

A popular nonparametric measure of a monotone relation between two variables is Kendall's tau. Originally, most analysis of this statistic assumed the two variables were independent, while more recently there has been interest in finding "nonnull" models for the observations which allow types of dependence. One such model popularized by Mallows (1957, Annals of Mathematical Statistics) uses a one-parameter exponential family model with the canonical sufficient statistic being equivalent to Kendall's tau.