Liu估计提出了线性回归模型的一种新的有偏估计:β(d)=(X′X+I)^-1(X′X+d)β,其中β=(X′X)^-1 X′Y是最小二乘估计,在此基础上提出了一种适应范围更广的有偏估计即广义Liu估计:β(D)=(X′X+I)^-1(X′X+D)β,D=diag(d1,d2,…,dp),其中0〈di〈1,并讨论了它的优良性。
A kind of biased estimator-Liu estimator was proposed. A new biased estimator in linear model-general Liu estimator is considered. In the sense of mean square error matrix, some properties of the general Liu estimation are obtained.