线性变换对带约束奇异线性模型的条件G-M估计的影响  

The Influence of the Condition G-M Estimation with Linear Transformation in Restricted Singular Linear Model

作　　者：章前[1] 

机构地区：[1]昆明理工大学管理工程系,昆明650093

出　　处：《应用数学》1998年第4期49-52,共4页Mathematica Applicata

摘　　要：考虑带约束奇异线性模型Y=Xβ＋ε，Lβ＝0，E（ε）＝0，cov（ε）＝σ²V，其中V为非负定矩阵，X为任意秩．文章研究了观察向量Y的线性变换对回归系数条件可估函数Sβ的G－M估计的影响，并将条件可估子空间μ（X’L’）划分成Ω＋Ω_＋Ω₂.当μ（S’）Ω时，Sβ的条件G-M估计在模型变化后其优良性不变；当μ（S’）Ω₁时，模型变化后Sβ仍可估，但Sβ的条件G－M估计的方差要变大；当μ（S’）Ω₂时，Sβ不可估．Consider restricted singular linear model Y = Xβ+ ε, Lβ= 0, E(β) = 0, coy (ε) =σ~2v, where V is a nonnegative matrix, and the rank of X is arbitrary. The paper studies the influence of the G-M estimation of regression coefficient condition estimable founction Sβ with the linear- transformation of observable vector Y, furthermore, divides the condition estimable subspace μ(X L)into when μ(S')Ω holds, the excellence of the condition G-M estimation of Sβ willbe preserved after the model has changed k； when μ(S')Ω, holds, Sβ is still estimable after the model changing, but the variance of condition G-M estimation will become greater; when μ(S')Ω_2 holds, Sβ is not estimable.

关 键 词：奇异线性模型 G-M估计 条件可估子空间 线性变换 

分 类 号：O212.1[理学—概率论与数理统计]