Slash-elliptical nonlinear regression model

Abstract

The aim of this paper is to develop nonlinear regression models with error distribution having the slash-elliptical family. A slash-elliptical random variable is defined as the quotient of two independent random variables, $Z$ and $U^{1/q}$, where $Z$ has an elliptical contoured distribution and $U$ has a uniform distribution. A key advantage of the slash-elliptical distribution is the simplicity by which the well-known elliptical contoured distribution can be modified to support increase in kurtosis. The main properties of the slash-elliptical distribution is symmetry, heavy tails and convergence to the elliptical contoured distribution as the limiting case of the shape parameter. One of the advantages of this distribution is to allow larger kurtosis than the elliptical contoured distribution. In this paper, we propose estimation method, residual analysis and generalized leverage for the new class of regression models. We also develop diagnostic measures under local influence approach and present a real data analysis.