Improved Estimation in Regression With Varying Penalty

This article considers the estimation of the intercept parameter of a simple linear regression model under asymmetric linex loss. The least-squares estimator (LSE) and the preliminary test estimator (PTE) are defined. The risk functions of the estimators are derived. The moment-generating function (MGF) and the first two moments of the PTE are shown. The risk of the PTE is compared with that of the LSE. The analyses show that if the nonsample prior information about the value of the parameter is not too far from its true value, the PTE dominates the traditional LSE.