Improved Estimation of Coefficient Vector in a Regression Model

Abstract

In this article we consider the problem of estimating the coefficient vector of a classical regression model when it is apriori suspected that the parameters vector may belong to a subspace. Two estimators; namely the positive-part of Stein-type estimator and the improved preliminary test estimator are proposed and it is demonstrated analytically as well as numerically that the proposed estimators dominate the usual Stein-type and pretest estimators respectively. The proposed estimators are also compared in terms of risks with that of the unrestricted estimator and we find that the positive-part of Stein-type estimator uniformly dominates the unrestricted estimator while the improved preliminary test estimator dominates the unrestricted estimator in a wider range than that of the usual pretest estimator.

Keywords:

• Uncertain prior information
• Quadratic biases
• Mean squared error matrices
• Risk functions
• Improved pretest estimator
• Positive-part of James–Stein estimator
• Percentage risk improvement

Acknowledgment

The authors are thankful to the referee for helpful comments on the earlier draft.