推广增长曲线模型及其参数矩阵在约束条件下的讨论  

Discussion on the Extensive Growth Curve Model under Restriction

作　　者：秦学军[1] 

机构地区：[1]武汉工业大学数学物理系

出　　处：《武汉工业大学学报》1993年第4期130-137,共8页

摘　　要：本文就推广增长曲线模型(the Extension of Growth Curve Model下简称EGC模型)其参数矩阵满足约束条件sum from i=1 to t E_iθ_iF'_i=0的情形进行讨论,得到参数矩阵一切可估线性组合的LS估计与GM估计相等的充要条件,以及相应于这两个估计的方差系数的两个估计值相等的充要条件,当约束条件中E_i=0或F_i=0(i=1,2,…,n)即得一般EGC模型结论。Considering the extensive growth curve model Y=sum from i=1 to t X_iθ_iM′_i+E, which perametric matrices are under restriction sum from i=1 to tE_iθ_iF′_i=0, if the linear combination of θ_i: sum from i=1 to tK_iθ_iL′_i,is estimable, we get the necessary and sufficient conditions on which the LS estimation and GM estimation of δ~2 are equal. Meanwhile,we obtain the condition on which two estimation of sum from i=1 to tK_iθ_iL′_i are equal. When the restriction is cancelled, conclusion about the growth curve model is generated.

关 键 词：增长曲线模型 最小二乘估计 GM估计 

分 类 号：O212.1[理学—概率论与数理统计]