线性混合模型中方差分量的估计与QR分解  

Estimation in the Mixed Linear Models and QR Decomposition

作　　者：范永辉[1] 王松桂[2] 

机构地区：[1]河北师范大学数信学院,石家庄050016 [2]北京工业大学应用数理学院,北京100022

出　　处：《应用概率统计》2008年第2期208-216,共9页Chinese Journal of Applied Probability and Statistics

基　　金：北京市属市管高等学校人才强教计划资助项目.

摘　　要：在线性混合模型中,极大似然估计是一种很重要的估计方法,但是它常常需要通过迭代求解.应用设计阵的QR分解,可以把设计阵变换成上三角矩阵.这样可以降低参与迭代运算的矩阵的阶数,还可以减少参与运算的数据量,从而提高运算的速度.本文讨论了QR分解在EM算法中的应用,并用模拟的方法验证了QR分解可以极大的提高运算的速度.本文同时讨论了QR分解在另外一种估计方法,即ANOVA估计中的应用.Maximum likelihood estimation is one of the most important estimate methods in the mixed linear models, but to get the maximum likelihood estimates of variance components we must use iterative algorithms in the most cases. The QR decomposition transforms the design matrices into upper-triangle matrix, then we can decrease the orders of the matrices used in the iterative process, and reduce the amount of data in this process. By simulation, we show that QR decomposition can make EM algorithm run much more quickly and get almost the same results we get without QR decomposition. We also study the ANOVA estimation with QR decomposition.

关 键 词：QR分解 极大似然估计 限制极大似然估计 EM算法 ANOVA估计 

分 类 号：O212.1[理学—概率论与数理统计]