The author considers a consistent, Kolmogorov-Smirnov type of test of the complete set of restrictions that relate to the copula representation of positive quadrant dependence. For such a test, he proposes and justifies inference relying on a simulation-based multiplier method and a bootstrap method. He also explores the finite-sample behaviour of both methods with Monte Carlo experiments. A first empirical illustration is given for American insurance claim data. A second one examines the presence of positive quadrant dependence in life expectancies at birth of males and females across countries.