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February 2017 Slash-elliptical nonlinear regression model
Izabel Cristina Alcantara, Francisco José A. Cysneiros
Braz. J. Probab. Stat. 31(1): 87-110 (February 2017). DOI: 10.1214/15-BJPS304

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.

Citation

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Izabel Cristina Alcantara. Francisco José A. Cysneiros. "Slash-elliptical nonlinear regression model." Braz. J. Probab. Stat. 31 (1) 87 - 110, February 2017. https://doi.org/10.1214/15-BJPS304

Information

Received: 1 October 2014; Accepted: 1 November 2015; Published: February 2017
First available in Project Euclid: 25 January 2017

zbMATH: 1362.62137
MathSciNet: MR3601662
Digital Object Identifier: 10.1214/15-BJPS304

Keywords: local influence , nonlinear model , residual , Slash-elliptical distribution

Rights: Copyright © 2017 Brazilian Statistical Association

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Vol.31 • No. 1 • February 2017
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