Linear regression models with slash-elliptical errors

Abstract

We propose a linear regression model with slash-elliptical errors. The slash-elliptical distribution with parameter q is defined as the ratio of two independent random variables Z and U1q, where Z has elliptical distribution and U has uniform distribution in (0,1). The main feature of the slash-elliptical distribution is to have greater flexibility in the degree of kurtosis when compared to the elliptical distributions. Other advantages of this distribution are the properties of symmetry, heavy tails and the inclusion of the elliptical family as a limit case when q→∞. We develop the methodology of estimation, hypothesis testing, generalized leverage and residuals for the proposed model. In the analysis of local influence, we also develop the diagnostic measures based on the likelihood displacement under the some perturbation schemes. Finally, we present a real example where slash-Student-t model is more stable than other considered models.