线性回归模型的一种有偏估计

A New Class of Biased Estimate in the Linear Regression Model

在线性回归模型Y=Xβ+ε;E(ε)=0;cov(ε)=σ2V;V>0下给出了有偏估计βh*=(XTV-1X+hI)-1(XTV-1Y+β*),其中h>0为参数,β*表示线性回归模型的广义最小二乘估计.讨论了这种有偏估计的优良性质,并证明了其可容许性,推广了已有的有关结果.

In the linear regression model Y=Xβ＋ε;E（ε）=0;cov（ε）=σ^2V;V〉0, this paper gives another class of biased estimate βh^＋=（X^T V^-1 X＋hI）^-1 （X^TV^-1Y＋β^＋）,where h〉0 is a parameter and ,β^＋ is the generlized least squares estimate, We proved βh^＋ was an admissible estimate with mang good characters .