Flexible Multivariate Density Estimation with Marginal Adaptation

Details Flexible Multivariate Density Estimation with Marginal Adaptation Flexible Multivariate Density Estimation with Marginal Adaptation

2009-01-02

arxiv.org/abs/0901.0225v1

Statistics

Methodology

23 pages, 1 Figure

Scientific paper

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.

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