Comparisons of variance estimators in a misspecified linear model with elliptically contoured errors

In a misspecified linear regression model with elliptically contoured errors, the exact biases and risks of least squares, restricted least squares, preliminary test and Stein-type estimators of the error variance are derived. Also, we compare the risk performances of the underlying estimators and give the dominance pictures for them. It is shown that the risk of preliminary test estimator attains the smallest value if the critical value equals one. Moreover, we give a bootstrap procedure for estimating the risks of proposed estimators in order to overcome the difficulty of computing the exact risks when the sample size becomes larger.