Flexible Multivariate Density Estimation with Marginal Adaptation

TL;DR

This paper introduces two novel estimators for multivariate density estimation that combine the strengths of mixture of normals and copula models, aiming for flexible and accurate marginal estimation.

Contribution

It proposes a mixture of normals copula model and a marginally adapted mixture of normals estimator, enhancing flexibility and marginal accuracy over existing methods.

Findings

Copula-based estimators can outperform or underperform compared to mixture models depending on data properties.

The proposed estimators are fast, reliable, and effective on both simulated and real datasets.

Empirical results demonstrate improved marginal and joint density estimation.

Abstract

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.