  This paper proposes a regression tree procedure to estimate conditional
copulas. The associated algorithm determines classes of observations based on
covariate values and fits a simple parametric copula model on each class. The
association parameter changes from one class to another, allowing for
non-linearity in the dependence structure modeling. It also allows the
definition of classes of observations on which the so-called "simplifying
assumption" [see Derumigny and Fermanian, 2017] holds reasonably well. When
considering observations belonging to a given class separately, the association
parameter no longer depends on the covariates according to our model. In this
paper, we derive asymptotic consistency results for the regression tree
procedure and show that the proposed pruning methodology, that is the model
selection techniques selecting the appropriate number of classes, is optimal in
some sense. Simulations provide finite sample results and an analysis of data
of cases of human influenza presents the practical behavior of the procedure.
