Nonnegative Minimum Biased Quadratic Estimation in the Linear Regression Models

摘要

In the paper the problem of norxnegative estimation of βHβ+hσ~2in the linear model E(y)=Xβ,Var(y)σ~2I is discussed. Here H is a nonnegative definite matrix while A is a nonncgativo scalar. An iterative procedure for the nonnegative minimum biased quadratic estimator is described. Moreover, in the case that H and X'X commute, an explicit formula for this estimator is given. Admissihility of the estimator is proved. The results arc applied to nonncgative estimation of the total moan squared error of a linear biased estimator.