Optimal Critical Values of a Preliminary Test for Linear Restrictions in a Regression Model with Multivariate Student-t Disturbances

Applied researchers typically pre-test to decide the final estimator of the coefficients in a regression model. Brook (1976) shows that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom, according to a mini-max (risk) regret criterion, when the prior test is of the validity of restrictions on the model's coefficients. Brook's result depends on the often unrealistic assumption of normally distributed disturbances. We consider the wider family of multivariate Student-t disturbances