基于Cholesky分解的协方差矩阵估计  

Covariance matrix estimation based on Cholesky decomposition

作　　者：褚云通 CHU Yuntong(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《高师理科学刊》2020年第9期11-16,共6页Journal of Science of Teachers＇College and University

摘　　要：重复测量数据经常在心理学、社会科学、经济学和医学研究等领域出现.对于重复测量数据,高维(HD)和正定(PD)约束是协方差和相关矩阵建模的2个主要障碍.基于Cholesky型分解的方法在处理HD和PD问题上是有效的.基于修正的Cholesky分解(MCD)、替代Cholesky分解(ACD)和Cholesky因子参数化(HPC)3种方法,对遵循高斯分布的重复测量数据拟合联合均值和方差模型,然后对参数估计的协方差矩阵进行了比较.Longitudinal data are often used in fields such as psychology,social science,economics and medical research,etc.For longitudinal data,high dimensional(HD)and positive definite(PD)constraints are two major obstacles to covariance and correlation matrix modeling.It is evident that Cholesky-type decomposition based methods are effective in dealing with HD and PD problems.Based on the modified Cholesky decomposition(MCD),alternating Cholesky decomposition(ACD)and hyperspherical parameterization of Cholesky factor(HPC)methods.The joint mean and variance models was fitted to the repeated measurement data following Gaussian distribution,and then the covariance matrices of parameter estimation was compared.

关 键 词：CHOLESKY分解 协方差矩阵估计 重复测量数据 

分 类 号：O212[理学—概率论与数理统计]