Improved likelihood inference in Birnbaum–Saunders regressions

The Birnbaum–Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved pp-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application.