Copula-type Estimators for Flexible Multivariate Density Modeling using Mixtures

TL;DR

This paper introduces flexible copula-type estimators for multivariate density modeling that separate marginal and joint dependence modeling, using mixture models and Variational Bayes algorithms, outperforming traditional copulas.

Contribution

It proposes a novel iterative estimation scheme for copula-type models that enhances flexibility beyond traditional copulas, with automatic model selection via Variational Bayes.

Findings

Outperforms traditional copulas in simulations

Demonstrates effectiveness on real datasets

Provides flexible density estimation framework

Abstract

Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the marginals of the joint dependence structure is known. This can only be done for a restricted set of copulas, e.g. a normal copula. Our article introduces copula-type estimators for flexible multivariate density estimation which also allow the marginal densities to be modeled separately from the joint dependence, as in copula modeling, but overcomes the lack of flexibility of most popular copula estimators. An iterative scheme is proposed for estimating copula-type estimators and its usefulness is demonstrated through simulation and real examples. The joint dependence is is modeled by mixture of normals and mixture of normals factor analyzers models, and mixture of t and mixture of t factor analyzers models. We develop efficient Variational Bayes algorithms for fitting these in which model selection is performed automatically. Based on these mixture models, we construct four classes of copula-type densities which are far more flexible than current popular copula densities, and outperform them in simulation and several real data sets.