标题： 灵活的多元密度估计与边缘适应 显示英文标题

标题： Flexible Multivariate Density Estimation with Marginal Adaptation

摘要： 本文研究了灵活估计多元密度的同时正确估计其边缘分布的问题。我们通过提出两种新的估计器来实现这一点，这两种估计器试图捕捉正态混合模型和copula估计器的最佳特性，同时避免它们的一些缺点。我们提出的第一个估计器是一种正态混合copula模型，它是正态和t copula等参数化copula模型的灵活替代方案。第二个是一种边缘调整的正态混合模型估计器，它通过利用边缘密度的单变量估计中的信息改进了标准的正态混合模型估计器。我们实证表明，基于copula的方法的表现可能比基于正态混合模型的估计器好得多或差得多，具体取决于数据的性质。我们提供了这些估计器的快速且可靠的实现，并在模拟数据和真实数据上展示了该方法学。 显示英文摘要

摘要： 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.