纵向数据下精度矩阵的替代的修正Cholesky分解

Alternative modified Cholesky decomposition of the precision matrix of longitudinal

纵向数据下相关系数矩阵可能具有科学意义。然而,在精度矩阵具有典型结构时,很少有文献同时关注对模型误识别稳健的相关系数矩阵估计和对于数据中离群值的稳健性。本文中我们为纵向数据的精度矩阵提出了一种替代的修正Cholesky分解(alternative modified Cholesky decomposition, AMCD),从而得到了关于新息方差模型误识别稳健的相关系数矩阵估计。我们建立了基于多元正态分布和AMCD的联合均值-协方差模型,发展了拟Fisher得分算法,证明了其极大似然估计的相合性和渐近正态性。进一步,我们建立了基于多元Laplace分布和AMCD的双稳健联合建模方法,为其极大似然估计发展了拟Newton算法。模拟研究和实际数据分析验证了所提AMCD方法的有效性。

The correlation matrix might be of scientific interest for longitudinal data.However,few studies have focused on both robust estimation of the correlation matrix against model misspecification and robustness to outliers in the data,when the precision matrix possesses a typical structure.In this paper,we propose an alternative modified Cholesky decomposition(AMCD)for the precision matrix of longitudinal data,which results in robust estimation of the correlation matrix against model misspecification of the innovation variances.A joint mean-covariance model with multivariate normal distribution and AMCD is established,the quasi-Fisher scoring algorithm is developed,and the maximum likelihood estimators are proven to be consistent and asymptotically normally distributed.Furthermore,a double-robust joint modeling approach with multivariate Laplace distribution and AMCD is established,and the quasi-Newton algorithm for maximum likelihood estimation is developed.The simulation studies and real data analysis demonstrate the effectiveness of the proposed AMCD method.