Multivariate nonparametric tests for independence

AbstractMultivariate generalizations of Bhuchongkul's bivariate rank statistics [Ann. Math. Statist.35 (1964)] have been introduced and studied in this paper for the purpose of testing mulitvariate independence. It is shown that the test statistics can be expressed as rank statistics which are easy to compute, have asymptotic normal distributions, and can detect mutual dependence in alternatives which are pairwise independent. The tests are compared to the Puri-Sen-Gokhale [Sankyha Ser. A32 (1970)] tests and a normal theory test [Anderson, “An Introduction to Statistical Analysis,” Wiley, 1958] using Pitman efficiency