  Our article addresses the problem of flexibly estimating a multivariate
density while also attempting to estimate its marginals correctly. We do so by
proposing two new estimators that try to capture the best features of mixture
of normals and copula estimators while avoiding some of their weaknesses. The
first estimator we propose is a mixture of normals copula model that is a
flexible alternative to parametric copula models such as the normal and t
copula. The second is a marginally adapted mixture of normals estimator that
improves on the standard mixture of normals by using information contained in
univariate estimates of the marginal densities. We show empirically that copula
based approaches can behave much better or much worse than estimators based on
mixture of normals depending on the properties of the data. We provide fast and
reliable implementations of the estimators and illustrate the methodology on
simulated and real data.
