时序相依数据的一种基于约束Cholesky分解的简约Gauss copula建模方法  

Parsimonious Gaussian copula modelling through constrained Cholesky decomposition for data with temporal dependence

作　　者：张伟平 李叶蓁 陈昱 汤琤咏 Weiping Zhang;Yezhen Li;Yu Chen;Chengyong Tang

机构地区：[1]中国科学技术大学管理学院,合肥230026 [2]Fox School of Business,Temple University,Philadelphia,PA 19122,USA

出　　处：《中国科学：数学》2023年第5期777-790,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12171450)资助项目。

摘　　要：对具有时序相依性的离散数据,本文从隐变量的角度使用Gauss copula建模.不同于现有方法,本文对协方差提出一种新的约束以实现Gauss copula模型的可识别性,并基于此提出一个新的隐变量框架对隐Gauss变量的方差和协方差进行简约建模,从而将基于修正的Cholesky分解的联合建模方法推广到广义线性模型中,建立相应的理论性质.模拟和实际数据分析验证了所提出方法的性能.Using the Gaussian copula modelling device from a perspective of latent variables,we consider the parsimonious modelling of generic types of data with the temporal dependence including those sequential observations being binary,categorical,and more.Different from the existing approaches,we directly investigate the covariance modelling in which a new kind of constraint is naturally developed to enable the identifiability of the latent Gaussian copula model.Then we develop a new latent variable framework concerning parsimoniously modelling the marginal means,variances,and covariances of the latent Gaussian variables with appealing practical interpretations.Our new framework broadly extends the joint mean-covariance modelling approaches based on the modified Cholesky decompositions to the regression analysis with broad types of response variables.Theoretical properties are then established for the resulting estimators of the parsimonious model.We demonstrate the performance of the proposed approaches with simulations and the real data analysis.

关 键 词：COPULA 协方差矩阵 修正的Cholesky分解 时序相依 加权成对似然 

分 类 号：O212.1[理学—概率论与数理统计]