Performance of Preliminary Test Estimator Under Linex Loss Function

Abstract

This article studies the performance of the unrestricted estimator (UE) and preliminary test estimator (PTE) of the slope parameter of simple linear regression model under linex loss function. The risk functions of both the UE and PTE are derived. The moment generating function (MGF) of the PTE is derived which turns out to be a component of the risk function. From the MGF the first two moments of the PTE are obtained and found to be identical to that obtained by using a different approach in Khan et al. (2002). The performance of the PTE is compared with that of the UE by using the analytical and graphical as well as the numerical methods. It is revealed that if the uncertain non sample prior information about the value of the slope is not too far from its true value then the PTE outperforms the UE.