摘要
对随机效应线性模型（y,X<sub>0</sub>β,Aα,σ<sup>2</sup>V）:y=x<sub>0</sub>β+ε,E（<sub>ε</sub><sup>β</sup>）=（A<sub>α</sub>/0）,Cov（<sub>ε</sub><sup>β</sup>）（?）给出了下列问题的解:当且仅当 X 满足什么条件时,才能使（y,X<sub>0</sub>β,Aα,σ<sup>2</sup>V）下任一可估函数ω′<sub>1</sub>α（或ω′<sub>2</sub>β或ω′<sub>1</sub>α+ω′<sub>2</sub>β）的所有 BLUE 都是（1）（y,xβ,Aα,σ<sup>2</sup>V）下ω′<sub>1</sub>α（或ω′<sub>2</sub>β或ω′<sub>1</sub>α+ω′<sub>2</sub>β）的线性无偏估计（LUE）或 BLUE（2）（y,Xβ,Aα,σ<sup>2</sup>V）下ω′<sub>1</sub>α（或ω′<sub>2</sub>β或ω′<sub>1</sub>α+ω′<sub>2</sub>β）的线性最小偏差估计（LIMBE）或最佳线性最小偏差估计（BLIMBE）
Consider a random effects linear model(y,X_0β,Aα,σ~2V):y=X_0β+ε,E(_ε~β)=(A_α/0),■We give the solutions to the following problems:What is X such that every BLUE of every estimable function ω′_1 α,ω′_2βor ω′_1α+ω′_2βunder(y,X_0β,Aα,σ~2V)is(1)a LUE or a BLUE under(y,Xβ,Aα,σ~2V);(2) a LIMBE or a BLMBE under(y,Xβ,Aα,σ~2V).We also give the solutions to the above-mentioned problens When attention is restricted to a subclass of estimable funetions.
