Improved log-Birnbaum-Saunders inference under type II censoring

Abstract

In this article, we report the development of adjustments to the profile likelihood function based on the proposals of Severini [Severini, T. A., 2000. Likelihood Methods in Statistics] and Cox and Reid [Cox, D.R., Reid, N. 1987. Parameter orthogonality and approximate conditional inference 49, 1-39] in the log Birnbaum-Saunders regression model under both type II censoring and noncensoring. We obtained the profile and modified profile maximum likelihood estimators, calculated the confidence intervals of the asymptotic type and bootstrap percentile and conducted tests based on profile and modified profile likelihood ratio statistics. Through Monte Carlo simulations, we numerically evaluated the behaviors of point estimators under different scenarios, as well as the performance of the likelihood ratio tests based on the profile and modified profile likelihoods, in terms of size and power. The results showed that both the tests and the estimators based on modified versions of the profile likelihood developed had superior performance in small samples in comparison with the estimators based on the unmodified version. Finally, an application to real data is presented.