Pre-Testing for Linear Restrictions in a Regressional Model with Student-t Errors

In this paper, we derive the exact risk (under quadratic loss) of pre-test estimators of the prediction vector and error variance of a linear regression model whose errors are assumed to be normally distributed but in fact follow a multivariate Student-t distribution. 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. Numerical evaluations of the risk expressions suggest that misspecifying the error distribution in this way does not, qualitatively, affect the risk properties of the estimators.