Influence diagnostics in Birnbaum–Saunders nonlinear regression models

Abstract

We consider the issue of assessing influence of observations in the class of Birnbaum–Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum–Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

Keywords:

• Birnbaum–Saunders distribution
• fatigue life distribution
• influence diagnostic
• generalized leverage
• lifetime data
• local influence
• maximum-likelihood estimation

Acknowledgements

We gratefully acknowledge grants from FAPESP (Brazil). The authors are also grateful to a referee for helpful comments and suggestions.