Improved likelihood-based inference in Birnbaum–Saunders nonlinear regression models

Abstract

We address the issue of performing testing inference in Birnbaum–Saunders nonlinear regression models when the sample size is small. The likelihood ratio, Wald and score statistics provide the basis for testing inference on the parameters in this class of models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction in matrix notation for the score test, which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald and score tests, and with the Bartlett-corrected likelihood ratio test, and bootstrap-corrected tests. Our simulation results suggest that the proposed corrected test can be an interesting alternative to other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.