Estimation of the Slope Parameter for Linear Regression Model with Uncertain Prior Information

The estimation of the slope parameter of the linear regression model with normal error is considered in this paper when uncertain prior information on the value of the slope is available. Several alternative estimators are defined to incorporate both the sample as well as the non-sample information in the estimation process. Some important statistical properties of the restricted, preliminary test, and shrinkage estimators are investigated. The performances of the estimators are compared based on the criteria of unbiasedness and mean square error. Both analytical and graphical methods are explored. None of the estimators is found to be uniformly superior over the others. However, if the non-sample information regarding the value of the slope is close to its true value, the shrinkage estimator over performs the rest of the estimators.