Shrinkage estimation of the regression parameters with multivariate normal errors

Abstract

In the linear model y=XB+e with the errors distributed as normal, we obtain generalized least square (GLS), restricted GLS (RGLS), preliminary test (PT), Stein-type shrinkage (S) and positive-rule shrinkage (PRS) estimators for regression vector parameter \beta when the covariance structure in known. We compare the quadratic risks of the underlying estimators and propose the dominance orders of the five estimators.

Keywords

• gls estimator
• preliminary test estimator
• stein-type shrinkage estimator
• positive-rule shrinkage estimator