纵向数据时间依赖性建模：多元几何偏正态 copula 的应用
Modeling temporal dependency of longitudinal data: use of multivariate geometric skew-normal copula
AI总结：
本文基于 MGSN 分布构建几何偏正态 copula，以刻画非高斯纵向数据的不可交换与尾部时间依赖，并支持连续、离散及有序 probit 回归的复合似然推断。
摘要：
近年来，使用 copula 对依赖性进行建模受到了广泛关注。另一方面，寻找具有理想依赖性质的多元 copula 也是一个重要的研究领域。在对非高斯纵向数据拟合回归模型时，通常使用多元高斯 copula 来处理重复测量的时间依赖性。但使用对称的多元高斯 copula 并非在所有情况下都可取，因为如果数据中存在不可交换依赖或尾部依赖，它无法捕捉这些特征。因此，为确保可靠推断，超越高斯依赖假设进行探索十分重要。本文基于 Kundu（2014）和 Kundu（2017）提出的多元几何偏正态（multivariate geometric skew-normal，MGSN）分布，构建几何偏正态 copula，以建模非高斯纵向数据的时间依赖性。我们首先研究所提出多元 copula 的理论性质，随后为连续型和离散型纵向数据分别开发回归模型。该 copula 的分位数函数独立于其对应多元分布的相关矩阵，因此与 Azzalini 和 Valle（1996）从偏椭圆分布导出的 copula 类别相比，在似然推断方面具有计算优势。此外，该多元 copula 可以进行复合似然推断，从而便于从具有与几何偏正态分布相同依赖结构的有序 probit 模型中估计参数。我们开展了大量模拟研究以验证所提出的模型，并将其应用于分析两个真实世界数据集的纵向依赖性。最后，我们报告了研究结果，说明其相对于基于多元高斯 copula 的回归模型所取得的改进。
英文摘要：
Use of copula for the purpose of modeling dependence has been receiving considerable attention in recent times. On the other hand, search for multivariate copulas with desirable dependence properties also is an important area of research. When fitting regression models to non-Gaussian longitudinal data, multivariate Gaussian copula is commonly used to account for temporal dependence of the repeated measurements. But using symmetric multivariate Gaussian copula is not preferable in every situation, since it can not capture non-exchangeable dependence or tail dependence, if present in the data. Hence to ensure reliable inference, it is important to look beyond the Gaussian dependence assumption. In this paper, we construct geometric skew-normal copula from multivariate geometric skew-normal (MGSN) distribution proposed by Kundu (2014) and Kundu (2017) in order to model temporal dependency of non-Gaussian longitudinal data. First we investigate the theoretical properties of the proposed multivariate copula, and then develop regression models for both continuous and discrete longitudinal data. The quantile function of this copula is independent of the correlation matrix of its respective multivariate distribution, which provides computational advantage in terms of likelihood inference compared to the class of copulas derived from skew-elliptical distributions by Azzalini & Valle (1996). Moreover, composite likelihood inference is possible for this multivariate copula, which facilitates to estimate parameters from ordered probit model with same dependence structure as geometric skew-normal distribution. We conduct extensive simulation studies to validate our proposed models and therefore apply them to analyze the longitudinal dependence of two real world data sets. Finally, we report our findings in terms of improvements over multivariate Gaussian copula based regression models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
