Truly Multivariate Structured Additive Distributional Regression
针对高维响应变量，提出一种基于高斯Copula的多元分布回归模型，允许各边缘分布灵活建模且依赖结构随协变量变化，通过贝叶斯收缩先验实现估计，在儿童营养不良和柏林交通检测数据中验证了有效性。
Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary parametric distribution is modelled through covariates. While such models have been developed for univariate and bivariate responses, the truly multivariate case remains extremely challenging for both computational and theoretical reasons. Alternative approaches to GAMLSS may allow for higher-dimensional response vectors to be modelled jointly but often assume a fixed dependence structure not depending on covariates or are limited with respect to modelling flexibility or computational aspects. We contribute to this gap in the literature and propose a truly multivariate distributional model, which allows one to benefit from the flexibility of GAMLSS even when the response has dimension larger than two or three. Building on copula regression, we model the dependence structure of the response through a Gaussian copula, while the marginal distributions can vary across components. Our model is highly parameterized but estimation becomes feasible with Bayesian inference employing shrinkage priors. We demonstrate the competitiveness of our approach in a simulation study and illustrate how it complements existing approaches along the examples of childhood malnutrition and a yet unexplored data set on traffic detection in Berlin.