An Exponentiated Skew-Elliptic Nonlinear Extension to the Log-Linear Birnbaum-Saunders Model with Diagnostic and Residual Analysis
An Exponentiated Skew-Elliptic Nonlinear Extension to the Log-Linear Birnbaum-Saunders Model with Diagnostic and Residual Analysis
Authors
Martinez-Florez, Guillermo
Gomez, Yolanda M.
Venegas, Osvaldo
Gomez, Yolanda M.
Venegas, Osvaldo
Profesor GuĆa
Authors
Date
Datos de publicaciĆ³n:
10.3390/axioms12070624
AXIOMS,Vol.12,2023
AXIOMS,Vol.12,2023
Tipo de recurso
Article
Keywords
Materia geogrƔfica
Collections
Abstract
In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model's parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented.