  Several procedures have been recently proposed to test the simplifying
assumption for conditional copulas. Instead of considering pointwise
conditioning events, we study the constancy of the conditional dependence
structure when some covariates belong to general borelian conditioning subsets.
Several test statistics based on the equality of conditional Kendall's tau are
introduced, and we derive their asymptotic distributions under the null. When
such conditioning events are not fixed ex ante, we propose a data-driven
procedure to recursively build such relevant subsets. It is based on decision
trees that maximize the differences between the conditional Kendall's taus
corresponding to the leaves of the trees. The performances of such tests are
illustrated in a simulation experiment. Moreover, a study of the conditional
dependence between financial stock returns is managed, given some clustering of
their past values. The last application deals with the conditional dependence
between coverage amounts in an insurance dataset.
