QR分解在方差分析中的应用

在线性混合模型的方差分量估计中，方差分析估计是一种很重要的估计方法。应用此方法估计过程中，所求的方程组的系数矩阵是上三角矩阵，很容易求得其解，然而它的计算会随着数据的增多变得既耗时又不稳定。用QR分解的方法计算方差分量的估计，不用计算投影阵及广义逆矩阵，而且参与运算的矩阵的阶数相对比较小，节约了存储空间。利用QR分解，讨论其在线性混合模型中方差分量的方差分析估计中的应用。

QR Decomposition for the Analysis Of Variance Estimate

The analysis of variance estimate is one of the most important estimate methods in the mixed linear models. When using this method to estimate variance components, the coefficient matrix of the equation is upper triangular matrix that is easy to find its solution, but its calculation becomes time - consuming and unstable as the number of data increases. Using QR decomposition to calculate variance component not only neednt calculate the projection matrix and generalized inverse matrix but also the order of the matrix is relatively small and saving storage space. This paper introduces QR decomposition and discusses its application in the analysis of variance estimate.