A Robust Birnbaum-Saunders Regression Model Based on Asymmetric Heavy-Tailed Distributions

• Activity Number: 245 - SLDS CSpeed 4
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Rocío Maehara* and Filidor Vilca and Heleno Bolfarine and Narayanaswamy Balakrishnan
• Companies: Universidad del Pacífico and Universidade Estadual de Campinas and Universidade de Sao Paulo and McMaster University
• Keywords: Nonlinear regression models; Birnbaum-Saunders distribution; EM-algorithm; Robust estimation; Skew-normal/Independent distribution; Sinh-normal distribution

Abstract

Skew-normal/independent distributions provide an attractive class of asymmetric heavytailed distributions to the usual symmetric normal distribution. We use this class of distributions here to derive a robust generalization of sinh-normal distributions (Rieck, 1989), we then propose robust nonlinear regression models, generalizing the BirnbaumSaunders regression models proposed by Rieck and Nedelman (1991) that have been studied extensively. The proposed regression models have a nice hierarchical representation that facilitates easy implementation of an EM-algorithm for the maximum likelihood estimation of model parameters and provide a robust alternative to estimation of parameters. Simulation studies as well as applications to a real dataset are presented to illustrate the usefulness of the proposed model as well as all the inferential methods developed here.