General linear estimators under the prediction error sum of squares criterion in a linear regression model

In this paper, the notion of the general linear estimator and its modified version are introduced using the singular value decomposition theorem in the linear regression model <bold>y</bold>=<bold>X</bold> <bold>β</bold>+<bold>e</bold> to improve some classical linear estimators. The optimal selections of the biasing parameters involved are theoretically given under the prediction error sum of squares criterion. A numerical example and a simulation study are finally conducted to illustrate the superiority of the proposed estimators.