  Thanks to their ability to capture complex dependence structures, copulas are
frequently used to glue random variables into a joint model with arbitrary
marginal distributions. More recently, they have been applied to solve
statistical learning problems such as regression or classification. Framing
such approaches as solutions of estimating equations, we generalize them in a
unified framework. We can then obtain simultaneous, coherent inferences across
multiple regression-like problems. We derive consistency, asymptotic normality,
and validity of the bootstrap for corresponding estimators. The conditions
allow for both continuous and discrete data as well as parametric,
nonparametric, and semiparametric estimators of the copula and marginal
distributions. The versatility of this methodology is illustrated by several
theoretical examples, a simulation study, and an application to financial
portfolio allocation.
