摘要
本文考虑协方差分析模型E(Y)=Xβ+ZυVAR(Y)=σ~2V V≥0其中,X、Z、V为已知,β、υ、σ~2(>0)为未知,给出了当Sβ+Qυ可估时,在平方损失函数下,Sβ+Qυ的齐次线性估计在齐次线性估计类中是可容许估计的充要条件和Sβ+Qυ的非齐次线性估计在非齐次线性估计类中是可容许估计的充要条件。
In this paper, we consider a covariance analysis model: E(Y)= Xβ + Zv,VAR(Y) =σ~2V,V≥0, where β∈R',v ∈R^q,and σ~2 >0 areall unknown, X, Z and V are known. Let Sβ + Qv be linearly estimable. Weobtain a necessary and sufficient condition for a homogeneous linear estimateof Sβ + Qv which is admissible in the class of all homogeneous linear estimatesunder a quadratic loss function,and the same result is for the inhomogeneouscase.
关键词
协方差分析
线性模型
参数
估计
covariance analysis
linear models
parameter
linear
estimations
admissibility
