Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances

In this paper we derive the exact risk (under quadratic loss) of pre-test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances. The pre-test in question is one of the validity of a set of exact linear restrictions on the model's coefficient vector. We demonstrate how the known results for the model with normal disturbances can be extended to this broader case. We also show that the critical value of unity results in a minimum of the risk of the pre-test estimator of the error variance. To illustrate the results we assume multivariate Student-t regression disturbances and numerically evaluate the derived expressions.