增长曲线模型非齐次线性估计的可容许性  

Admissibility of Nonhomogeneous Linear Estimators of Matrix Function under Matrix Loss Function in Growth Curve Model

作　　者：李俊海[1] 郎宏志 等 

机构地区：[1]郑州工业高等专科学校，河南郑州450007 [2]郑州轻工业学校基础部，河南郑州450007

出　　处：《郑州工业高等专科学校学报》2002年第3期38-40,共3页Journal of Zhengzhou Polytechnic Institute

摘　　要：讨论增长曲线模型Y＝X1BX2＋ε中回归矩阵B的函数C1BC2的估计L1YL2＋A，在矩阵损失[(L2^T2×L1）Y→＋A→－（S^T2X^T2×S1X1）B→][（L^2×L1）Y→＋A^→-(S^T2X^T2×S1X1）B→]^T下，我们得到了非齐次线性估计L1YL2＋A在非齐次线性估计类Г＝｛L1YL2＋A|L1:t×p,L2:t×p,L2;n×n，A：t×s均为已知实阵｝中可容许的充要条件：L1YL2在Г0＝｛L1YL2|L1:t×p,L2:n×s均为已知实阵｝中容许且当L^T2X^T2×L1X1=S^T2X^T2×S1X1时有A＝0。In this paper,we discuss L 1YL 2+A the nonhomogeneous liner estimator of C 1BC 2 the function of regression matrix B in growth curve model Y=X 1BX 2+ε , under matrix loss (1.3) ,we prove a nonhomogeneous liner estimator of L 1YL 2+A is admissible among the class of all nonhomogeneous liner estimators Г=｛L 1YL 2+A｜L 1:t×p,L 2;n×n,A:t×s known real martix｝ only and only that :L 1YL 2 is admissible among the liner estimators class of ｛L 1YL 2｜L 1:t×p,L 2:n×s known real martix｝ and when L T 2X T 2L 1X 1=S T 2X T 2S 1X 1 there is A=0.

关 键 词：非齐次线性估计 可容许性 增长曲线模型 矩阵损失 

分 类 号：O212[理学—概率论与数理统计]