Mixed Marginal Copula Modeling

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density of the observations with respect to a mixed measure. The treatment is quite general, although we focus on mixtures of Gaussian and Archimedean copulas. The inference is Bayesian with the estimation carried out by Markov chain Monte Carlo. We illustrate the methodology and algorithms by applying them to estimate a multivariate income dynamics model. Supplementary materials for this article are available online.

本文将关于带有离散或连续边缘分布的连接函数（copula）的研究文献拓展至部分边缘分布为离散与连续分量混合的情形。我们通过将似然函数严格定义为观测值关于混合测度的密度，完成了这一拓展。尽管本文重点聚焦于高斯（Gaussian）与阿基米德（Archimedean）连接函数的混合形式，但整体处理框架具备较强的一般性。推断环节采用贝叶斯方法，估计过程通过马尔可夫链蒙特卡洛（Markov Chain Monte Carlo）完成。我们通过将所提方法与算法应用于多元收入动态模型的估计，对其进行了演示验证。本文的补充材料可在线获取。