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

• Published in: Journal of statistical computation and simulation Vol. 75; no. 6; pp. 409 - 423
• Main Authors: Vasconcellos, Klaus L. P., Da Silva, Sydney Gomes
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01.06.2005; Taylor and Francis
• Subjects: Bias correction; Exact sciences and technology; Linear inference, regression; Mathematics; Maximum likelihood estimation; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Sciences and techniques of general use; Statistics; Student-t regression model; Unknown degrees of freedom; Freedom degree; Maximum likelihood estimation; Student test; Error estimation; Student-t regression model; Statistical method; Bias correction; Unknown degrees of freedom; Statistical computation; Regression model; Maximum likelihood; Small sample property; Biased estimation; Likelihood function
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949650412331270888

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.