In this paper, using the asymmetric LINEX loss function, we examine the risk performance of the ordinary least squares estimator (OLSE), two-stage Aitken estimator (2SAE) and pre-test estimator (PTE) after a pre-test for homoscedasticity in a linear regression model with possible heteroscedasticity. It is shown that the 2SAE is dominated by the PTE with the critical value of unity not only under the quadratic loss function but also under the asymmetric LINEX loss function.