Parsimonious graphical dependence models constructed from vines
Harry Joe · Canadian Journal of Statistics · 2018
Abstract Multivariate models with parsimonious dependence have been used for a large number of variables, and have mainly been developed for multivariate Gaussian. Graphical dependence model representations include Bayesian networks, conditional independence graphs, and truncated vines. The class of Gaussian truncated vines is a subset of Gaussian Bayesian networks and Gaussian conditional independence graphs, but has an extension to non‐Gaussian dependence with (i) combinations of continuous and discrete random variables with arbitrary univariate margins, and (ii) accommodation of latent variables. To illustrate the importance of graphical models with latent variables that do not rely on the Gaussian assumption, the combined factor‐vine structure is presented and applied to a data set of stock returns.The Canadian Journal of Statistics46: 532–555; 2018 © 2018 Société statistique du Canada