A Nonparametric Test for Independence Based on Sample Space Partitions
Olivier Thas, Jean‐Pierre Ottoy · Communications in Statistics - Simulation and Computation · 2004
In this paper, a class of nonparametric tests for independence between two continuous random variables is proposed. The members of the class are characterized by the size of the partitions of the sample space on which the test statistics are based. The test statistic that corresponds to the smallest partition size may be seen as an extension of Hoeffding's statistic with an Anderson–Darling-type weight function. In this simplest case, we have proven its asymptotic null distribution as well as its omnibus consistency. In a simulation study, the powers of the new tests are compared to those of some other tests for independence. It is concluded that overall high powers are obtained with these new tests.