Nonparametric positive quadrant dependence tests for copulas: A simulation comparison study

This work focuses on testing the null hypothesis of positive quadrant dependence (PQD) between two random variables. Such a testing problem is important since prior knowledge of positive quadrant dependence is a qualitative restriction that should be taken into account in further statistical analysis, for example- when choosing an appropriate copula function to model the dependence structure. The key methodology of the proposed testing procedures consists of evaluating a ‘distance’ between a nonparametric estimator of a copula and the independence copula, which serves as a reference case in the whole set of copulas having the positive quadrant dependence property. Choices of appropriate distances and nonparametric estimators of copula are discussed. A simulation study is carried out to investigate the finite sample size and power performances of three types of test statistics, Kolmogorov-Smirnov, Cram´er-von-Mises and Anderson-Darling statistics, alongside several nonparametric estimators of copula. Finally, the testing procedures has been applied on real data sets.