Estimation of the slope parameter in a linear regression model under a bounded loss function

The estimation of the slope parameter of a simple linear regression model in the presence of nonsample prior information under the reflected normal loss function is considered. Usually, the traditional estimation methods such as the least squared (LS) error are used to estimate the slope parameter. Sometimes the researcher has information about the unknown slope parameter from experience as a point guess, the nonsample prior information. In this paper, the shrinkage pretest estimators are introduced and their risk functions are derived under the reflected normal loss function. Several methods of finding distrust coefficient of the shrinkage pretest estimators are proposed. The behavior of the estimators are compared using a simulation study. The results show that the shrinkage pretest estimator outperforms the LS estimator when nonsample prior information is close to the real value. A real data set is analyzed for illustrating the results.