Corrected estimates for Student t regression models with unknown degrees of freedom

Abstract

We discuss analytical bias corrections for maximum likelihood estimators in a regression model where the errors are Student-t distributed with unknown degrees of freedom. We propose a reparameterization of the number of degrees of freedom that produces a bias corrected estimator with very good small sample properties. This unknown number of degrees of freedom is assumed greater than 1, to guarantee a bounded likelihood function. We discuss some special cases of the general model and present some simulations which show that the corrected estimates perform better than their corresponding uncorrected versions in finite samples.