An extension of the empirical copula is considered by combining an estimator
of a multivariate cumulative distribution function with estimators of the
marginal cumulative distribution functions for marginal estimators that are not
necessarily equal to the margins of the joint estimator. Such a hybrid
estimator may be reasonable when there is additional information available for
some margins in the form of additional data or stronger modelling assumptions.
A functional central limit theorem is established and some examples are
developed.Comment: 17 page
