In this paper, satisfactory estimation problem under constraint of regional pole index,H ∞index and error variance index for a class of linear stochastic systems is presented.

Study on the Restricted Biased Estimation in the Linear Model;

iscusses the problem of linear biased estimation of the parent mean.

To linear regression models Y=Xβ+ε,E(ε)=0,Cov(ε)=σ2V,V>0,the necessary and sufficient condition that biased estimation β*h=(XTV-1X+hI)-1(XTV-1Y+β*) is an admissible estimation is obtained and β*h condition that is superior to ridge estimation is also given.

A class of biased estimate of regression coefficients;

A new class of biased estimate in the multiple linear model;

In the linear regression model:Y=Xβ+ε,E(s)=0,cov(ε)=σ2v,v>0,reference [1] presented a biased estimate:β*s=(XTV-1X+sI)-1(XTV-1Y+β*),where s>0 was a parameter and β was the generalized least squares estimate.

For the linear model with aggregated data,this paper proposed two kinds of biased estimators which have some superiority to the unbiased estimators in the sense of mean square error.

1),an improved biased estimator is proposed in this paper.

In this paper,a new biased estimator-double k type ridge estimator(DKRE) is proposed to improve some existing biased estimators based on the peculiarity of ill-conditioning of the design matrix.

Aiming at the fundamental reason for the bad performance of the LS estimator of the coefficients in the linear regression models,presents the generalized c-K estimators of the coefficients,which combines various classical biased estimators into a bigger class of estimators and studies the improvement of the biased estimators.

Aiming at the fundamental reason for the bad performance of the LS estimator of the coefficients in the linear regression models,this paper presents the generalized c-K estimators of the coefficients,which combines various classical biased estimators into a bigger class of estimators and studies the improvement of the biased estimators.