The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function

Abstract

We examine the risk of a pre-test estimator for regression coefficients after a pre-test for homoskedasticity under the Balanced Loss Function (BLF). We show analytically that the two stage Aitken estimator is dominated by the pre-test estimator with the critical value of unity, even if the BLF is used. We also show numerically that both the two stage Aitken estimator and the pre-test estimator can be dominated by the ordinary least squares estimator when “goodness of fit” is regarded as more important than precision of estimation.

Keywords:

• balanced loss
• heteroskedasticity
• sequential estimator
• goodness of fit

Additional information

Notes on contributors

Kazuhiro Ohtani

David E. A. Giles