We discuss the so-called “simplifying assumption” of conditional copulas in a general framework. We introduce several tests of the latter assumption for non-and semiparametric copula models. Some related test procedures based on conditioning subsets instead of pointwise events are proposed. The limiting distribution of such test statistics are assessed by several bootstrap schemes, most of them being new. We prove the validity of a particular semi-parametric bootstrap scheme. Some simulations illustrate the relevance of our results.

This is a joint work with Alexis Derumigny (Crest).