A new method of spectral decomposition of covariance matrix in mixed effects models and its applications  

作　　者：WU Mixia WANG Songgui 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100022, China College of Applied Sciences, Beijing University of Technology, Beijing 100022, China

出　　处：《Science China Mathematics》2005年第11期1451-1464,共14页中国科学：数学（英文版）

基　　金：supported by the National Nature Science Foundation of China(Grant No.10271010);the Natural Science Foundation of Bejng(Grant No.1032001)

摘　　要：For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature,the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.

关 键 词：mixed effects model spectral decomposition analysis of variance estimate maximum LIKELIHOOD ESTIMATE 

分 类 号：N[自然科学总论]