Nonparametric Tests for Positive Quadrant Dependence

We consider distributional free inference to test for positive quadrant dependence, i.e. for the probability that two variables are simultaneously small (or large) being at least as great as it would be were they dependent. Tests for its generelisation in higher dimensions, namely positive orthant dependences, are also analysed. We propost two types of testing procedures. The first procedure is based on the specification of the dependence concepts in terms of distribution functions, while the second procedure exploits te copula representation. For each specification a distance est and an intersection-union test for inequality constraints are deveoped depending on the definition of null and alternative hypotheses. An empirical illustration is given for US and Danish insurance claim data. Practical implications for the design of reinsurance treaties are also discussed.