Pre-Testing in a Mis-Specified Regression Model

We consider the pre-test estimation of . the parameters of a linear regression model after a preliminary-test for exact linear restrictions when the model is mis-specified through the omission of relevant regressors and the usual assumption of normal regression disturbances is widened to a subclass of the family of spherically symmetric errors. We derive and analyse the exact risk (under quadratic loss) of a pre-test estimator of the prediction vector and of the scale parameter