Shrinkage pre-test estimator of the intercept parameter for a regression model with mulativariate student-t errors

Abstract

[Abstract]: In presence of an uncertain prior information about the slope parameter, the estimation of the intercept of a simple regression model with a multivariate Student-t error distribution is investigated. The unrestricted, restricted and preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiencies are analysed. A maximin criterion is established, and graphs and tables are constructed for different number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance levelis also discussed.