ESTIMATION OF THE ERROR VARIANCE AFTER A PRELIMINARY-TEST OF HOMOGENEITY IN A REGRESSION-MODEL WITH SPHERICALLY SYMMETRICAL DISTURBANCES

In this paper we consider the risk (under quadratic loss) of an estimator of the error variance after a pre-test for homogeneity of the variances in the two-sample linear regression model. We investigate the effects on risk of assuming normal disturbances when in fact the error distribution is spherically symmetric. We also broaden the standard assumption that the never-pool variance estimators are based on the least squares principle. To illustrate the results numerically we consider two families of variance mixing distributions, one of which results in multivariate Student-t disturbances. Our results show that in some situations we should always pre-test, even if the error variances are equal, and we provide the optimal test critical value. The evaluations also show that using the least squares technique to form the never-pool estimators may not always be the preferred strategy.