Nonparametric Tests for Positive Quadrant Dependence

We consider distributional free inference to test for positive quadrant dependence, that is, 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 generalization to higher dimensions, namely positive orthant dependence, are also analyzed. We propose 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 the copula representation. For each specification, a distance test and an intersection-union test for inequality constraints are developed for time-dependent data. An empirical illustration is given for U.S. insurance claim data, where we discuss practical implications for the design of reinsurance treaties. Another application concerns detection of positive quadrant dependence between the HFR and CSFB/Tremont market neutral hedge fund indices and the Samp;P 500 index