An Ordering for Positive Dependence

Abstract

In this paper we introduce a partial ordering for positive dependent bivariate distributions. Our main result shows that tests of independence based on rank statistics such as Spearman's rho, Kendall's tau, Fisher-Yates' normal score statistic, van der Waerden's statistic and the quadrant statistic become more powerful under increasing positive dependence. In other words, these measures of positive dependence preserve the ordering stochastically in samples whenever it is present between underlying distributions.