We consider a consistent test, that is similar to a Kolmogorov-Smirnov test, of the complete set of restrictions that relate to the copula representation of positive quadrant dependence. For such a test we propose and justify inference relying on a simulation based multiplier method and a bootstrap method. We also explore the finite sample behavior of both methods with Monte Carlo experiments. A first empirical illustration is given for US insurance claim data. A second one examines the presence of positive quadrant dependence in life expectancies at birth of males and females among countries.