线性回归模型Liu估计的新研究

The New Study of Liu Estimated in Linear Regressionmodel

考虑线性回归模型Y=Xβ+ε,E()ε=0,Cov()ε=2σI(1),当设计矩阵X的列存在共线性时,最小二乘估计^β=(X′X)-1X′Y的性质变坏,为此给出了有偏估计^(βK,d)=(X′X+K)-1(X′Y+d^β),其中K为对角矩阵,K=diag(k1,…kp),ki≥0,d>0为参数,讨论了这种有偏估计与广义岭估计、Liu估计的比较,并证明了其可容许性估计.

Consider the linear regression model Y=Xβ+ε,E(ε)=0,Cov(ε)=σ2I(1),when the design matrix X is in the presence of linear time,the nature of β^=(X′X)-1X′Y is bad.This paper gives another biased estimate β^(K,d)=(X′X+K)-1(X′Y+dβ^),where K is diagonal matrix,d>0 as parameters,discusses the biased estimates and estimates Generalized Ridge,Liu estimates,and justifies its admissible estimates.