Flexible Multivariate Density Estimation With Marginal Adaptation

Abstract

This article is concerned with multivariate density estimation. We discuss deficiencies in two popular multivariate density estimators—mixture and copula estimators, and propose a new class of estimators that combines the advantages of both mixture and copula modeling, while being more robust to their weaknesses. Our method adapts any multivariate density estimator using information obtained by separately estimating the marginals. We propose two marginally adapted estimators based on a multivariate mixture of normals and a mixture of factor analyzers estimators. These estimators are implemented using computationally efficient split-and-elimination variational Bayes algorithms. It is shown through simulation and real-data examples that the marginally adapted estimators are capable of improving on their original estimators and compare favorably with other existing methods. Supplementary materials for this article are available online.

Key Words:

• Copula
• Mixture of factor analyzers
• Mixture of normals
• Nonparametric
• Variational Bayes

ACKNOWLEDGMENTS

The research of Xiuyan Mun, Minh-Ngoc Tran, and Robert Kohn was partially supported by the Australian Research Council grant DP0667069. The authors thank Professor Wenxin Jiang for the current form of Lemma 1 and Professor Jasra for the genome data.