Improved Likelihood Inference in Birnbaum-Saunders Regressions

TL;DR

This paper improves likelihood inference in Birnbaum-Saunders regression models for small samples by introducing a correction to the likelihood ratio test, enhancing its reliability and accuracy.

Contribution

The authors develop a correction factor for the likelihood ratio test in Birnbaum-Saunders regressions, reducing size distortion in small samples.

Findings

Corrected test reduces size distortion in small samples.

Modified test outperforms the standard likelihood ratio test in finite samples.

Empirical application demonstrates practical effectiveness.

Abstract

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. We show that the likelihood ratio test tends to be liberal when the sample size is small, and we obtain a correction factor which reduces the size distortion of the test. The correction makes the error rate of he test vanish faster as the sample size increases. The numerical results show that the modified test is more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application.