Bartlett corrections in Birnbaum–Saunders nonlinear regression models

Abstract

Lemonte and Cordeiro [Birnbaum–Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441–4452] introduced a class of Birnbaum–Saunders () nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum–Saunders regressions, Comput. Stat. Data Anal. 54 (2010), pp. 1307–1316], which hold only for the ( linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

Keywords:

• Bartlett correction
• Birnbaum–Saunders distribution
• lifetime data
• maximum likelihood estimation
• nonlinear regression

Acknowledgements

We gratefully acknowledge grants from FAPESP and CNPq (Brazil), and Mobility Program of the Universidad Industrial de Santander (Colombia). We thank an anonymous referee for helpful comments.