A Class of Distribution-Free Tests for Independence Against Positive Quadrant Dependence

Abstract

A class of distribution-free tests based on convex combination of two U-statistics is considered for testing independence against positive quadrant dependence. The class of tests proposed by Kochar and Gupta (1987) and Kendall's test are members of the proposed class. The performance of the proposed class is evaluated in terms of Pitman asymptotic relative efficiency for Block-Basu (1974) model and Woodworth family of distributions. It has been observed that some members of the class perform better than the existing tests in the literature. Unbiasedness and consistency of the proposed class of tests have been established.