线性模型中参数估计的相对效率

对于一个线性模型,如果最小二乘估计(LSE)与最佳线性无偏估计(BLUE)相等,就可以放心地用LSE代替BLUE;反之,用LSE代替BLUE就要蒙受一些损失,有时,这种损失可能是很大的,因而研究这种损失的大小就显得颇为重要.考虑一般线性模型Y=Xβ+ε,E(ε)=0,cov(ε)=σ2∑,定义了LSE相对于BLUE的两个新的相对效率,并给出了它们的上界.

Relative Efficiency of the Parameter Estimate in the Linear Model

For one linear model , the best linear unbiased estimate( BLUE) can be substituted by the least square estimate( LSE) if they are equal to each other ; On the contrary , this method will bring some loss . Sometimes the loss is very great , so it,s very important to study the loss . For general linear modelY=Xβ+ε,E(ε)=0,cov (ε)=σ~2∑,two new relative efficiencies are given and the upper bounds are obtained.