发表机构
University of Göttingen（哥廷根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于正则藤蔓Copula的多元结构化加性分布回归模型，通过逐树随机变分推断实现可扩展估计，并利用有效自由度信息准则进行族和树选择，应用于荷兰气象数据展示依赖结构的非线性时空变化。
AI 中文摘要
结构化加性分布回归灵活地将条件响应分布的所有参数与协变量相关联，但当依赖结构复杂时，多元扩展仍具挑战性。我们提出了一种基于正则藤蔓Copula的多元结构化加性分布回归模型。不同的藤蔓边可以使用不同的pair-copula族，而每个pair-copula参数可以通过结构化加性预测因子随协变量变化。因此，该模型能够适应异质的边际分布，以及针对每对变量的非对称、尾部依赖和协变量依赖的依赖结构。为了可扩展的推断，我们开发了一种基于分量特定高斯变分近似的逐树随机变分推断程序。首先估计边际模型，然后沿藤蔓树顺序进行pair-copula回归。我们还通过拟合候选的协变量依赖pair-copula回归，并使用基于有效自由度的信息准则进行族和树选择，从而调整顺序藤蔓选择。在模拟中，逐树估计器接近使用真实递归条件输入的神谕，而全局细化产生更集中的近似，并对上游分量产生较低频率覆盖。对荷兰六维气象数据的应用产生了一个结合高斯和非高斯pair-copula的藤蔓，其依赖结构表现出显著的非线性空间和时间变化。
英文摘要
Structured additive distributional regression flexibly relates all parameters of a conditional response distribution to covariates, but multivariate extensions remain challenging when dependence is complex. We propose a multivariate structured additive distributional regression model based on regular vine copulas. Different vine edges may use different pair-copula families, while every pair-copula parameter may vary with covariates through a structured additive predictor. The model therefore accommodates heterogeneous marginal distributions together with pair-specific asymmetric, tail-dependent, and covariate-dependent dependence structures. For scalable inference, we develop a tree-wise stochastic variational inference procedure based on component-specific Gaussian variational approximations. Marginal models are estimated first, followed by pair-copula regressions sequentially along the vine trees. We also adapt sequential vine selection by fitting candidate covariate-dependent pair-copula regressions and using information criteria based on effective degrees of freedom for both family and tree selection. In simulations, the tree-wise estimator remains close to an oracle using the true recursive conditional inputs, whereas global refinement yields more concentrated approximations and lower frequentist coverage for upstream components. An application to six-dimensional meteorological data from the Netherlands yields a vine combining Gaussian and non-Gaussian pair copulas, with pronounced nonlinear spatial and temporal variation in dependence.
