含有随机效应的增长曲线模型协差阵的最小二乘估计

The least square estimate of covariance matrices in the growth curve model with random effects

利用矩阵的谱分解和投影理论,给出了增长曲线模型均值结构中存在随机效应时,随机效应和随机误差两种不同性质的随机变量的协差阵Γ,Σ及其线性函数tr(CΣ+DΓ)的最小二乘估计,并讨论了估计tr(CΣ*+DΓ*)的一些优良性。

In this paper, a least square estimate of the covariance matrices Σ, Γ and their linear function tr(CΣ+DΓ) of the growth curve model with random regression (coefficient) structure has been given respectively by using the projective theory and the spectrum decomposition of matrix. Finally, it gives some optimal properties of tr(CΣ\+*+DΓ\+*).