线性模型中一些有偏估计在MSE准则下的优良性

Superiorities for Some Biased Estimators in Linear Regression Model under MSE Criterion

对于线性回归模型Y=Xβ+,εE(ε)=0,cov(ε)=σ2V,V≥0,针对设计阵多重共线性问题,给出了回归系数的几个有偏估计,并讨论在MSE准则下优于广义最小二乘估计的条件,解决了复共线性的回归问题.

Considering linear regression models Y=Xβ＋ε,E（ε）=0,cov（ε）=σ^2V,V≥0 according to the approximate multicol-linearity of matrix, some biased estimators of regression coefficients are given,and the sufficient conditions are given,under which they are better than generalized least squares estimator under the MSE criterion,the problem of multivariate regression is also resolved.