Flexible Multivariate Density Estimation With Marginal Adaptation |
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Authors: | Paolo Giordani Xiuyan Mun Minh-Ngoc Tran Robert Kohn |
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Affiliation: | 1. Research Department , Sveriges Riksbank , Stockholm , SE , 103 37 , Sweden;2. Australian School of Business , University of New South Wales , Sydney , NSW , 2052 , Australia |
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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. |
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Keywords: | Copula Mixture of factor analyzers Mixture of normals Nonparametric Variational Bayes |
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