A new rank correlation measure

摘要

A new rank correlation measure β_n is proposed, so as to develop a nonparametric test of independence for two variables. β_n is shown to be the symmetrized version of a measure earlier proposed by Borroni and Zenga (Stat Methods Appl 16:289-308, 2007). More specifically, β_n is built so that it can take the opposite sign, without changing its absolute value, when the ranking of one variable is reversed. Further, the meaning of the population equivalent of β_n is discussed. It is pointed out that this latter association measure vanishes not only at independence but, more generally, at indifference, that is when the two variables do not show any "tendency" to positive or negative dependence. The null distribution of β_n needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of β_n is derived. Finally, the performance of the test based on β_n is evaluated by simulation. β_n is shown to be a good competitor of some classical tests for the same problem.