On testing for independence against right tail increasing in bivariate models

A random variableY is right tail increasing (RTI) inX if the failure rate of the conditional distribution ofX givenY>y is uniformly smaller than that of the marginal distribution ofX for everyy0. This concept of positive dependence is not symmetric inX andY and is stronger than the notion of positive quadrant dependence. In this paper we consider the problem of testing for independence against the alternative thatY is RTI inX. We propose two distribution-free tests and obtain their limiting null distributions. The proposed tests are compared to Kendall's and Spearman's tests in terms of Pitman asymptotic relative efficiency. We have also conducted a Monte Carlo study to compare the powers of these tests.Research supported by an NSERC Canada operating grant at the University of Alberta.Part of this research was done while visiting the University of Alberta supported by the NSERC Canada grant of the first author.