标题： 基于藤copula的依赖模式在多变量事件时间数据中的似然估计 显示英文标题

标题： Vine copula based likelihood estimation of dependence patterns in multivariate event time data

摘要： 在许多研究中，多元事件时间数据是从具有可能复杂关联模式的集群生成的。需要灵活的模型来捕捉这种依赖关系。藤copulas（ vines copulas）可以达到这个目的。对于完整数据，藤copulas的推断方法是可用的。然而，事件时间数据常常受到右删失的影响。因此，现有的推断工具，如似然估计，需要进行调整。提出了一种两阶段估计方法。首先，对边缘分布进行建模。其次，通过最大化似然函数来估计由藤copulas建模的依赖结构。由于存在右删失，copula的似然表达式中出现了单重和双重积分，因此需要数值积分来评估它。为了进行依赖性建模，提供了一种顺序估计方法，以简化似然优化的计算挑战。三维仿真研究提供了证据，证明所提出的方法在有限样本下的表现良好。使用四维乳腺炎数据，展示了如何为手头的数据选择合适的藤copulas模型。 显示英文摘要

摘要： In many studies multivariate event time data are generated from clusters having a possibly complex association pattern. Flexible models are needed to capture this dependence. Vine copulas serve this purpose. Inference methods for vine copulas are available for complete data. Event time data, however, are often subject to right-censoring. As a consequence, the existing inferential tools, e.g. likelihood estimation, need to be adapted. A two-stage estimation approach is proposed. First, the marginal distributions are modeled. Second, the dependence structure modeled by a vine copula is estimated via likelihood maximization. Due to the right-censoring single and double integrals show up in the copula likelihood expression such that numerical integration is needed for its evaluation. For the dependence modeling a sequential estimation approach that facilitates the computational challenges of the likelihood optimization is provided. A three-dimensional simulation study provides evidence for the good finite sample performance of the proposed method. Using four-dimensional mastitis data, it is shown how an appropriate vine copula model can be selected for data at hand.