向量藤连接函数模型用于多元纵向数据
Vector Vine Copula Models for Multivariate Longitudinal Data
- Melbourne Business School, University of Melbourne（墨尔本商学院，墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出向量可绘制藤（VD-vine）连接函数模型，将传统藤扩展到向量节点以处理多元纵向数据的非高斯边际和非线性序列依赖，通过递归条件传输实现高效推断，并在模拟和八波澳大利亚面板数据中验证了其预测优势。
AI中文摘要：
多元纵向数据可能表现出非高斯边际分布、非线性动态以及响应向量组成随波次变化的特点。为应对这些特征，我们引入了一种向量可绘制藤（VD-vine）连接函数，将传统的可绘制藤连接函数从标量节点扩展到向量值节点。在此框架下，每个波次的响应向量构成一个多元边际分布，序列相关性通过一系列连接向量连接函数来捕捉。我们证明了VD-vine本身就是一个向量连接函数，并且在标量节点情况下退化为传统的可绘制藤。我们推导了递归的前向和后向条件传输，使得似然评估和预测模拟高效可行，并在有限阶马尔可夫和平稳性约束下实现了简约化。高斯和FGM连接向量连接函数的无约束参数化、灵活的多元边际分布以及贝叶斯变分推断提供了实用的实现方案。模拟结果显示，当边际分布不对称且序列相关性为多元时，预测精度有所提高，而在正确指定的高斯面板向量自回归下损失很小。在一项包含1,093名个体、响应向量随波次变化的八波澳大利亚面板数据中，完整的VD-vine在所考虑的模型中提供了最佳的交叉验证分布预测，确立了捕捉不对称性和非线性依赖性的优势。
英文摘要：
Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1,093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence.
