Likelihood-based inference in censored exponential regression models

This paper deals with the issue of testing hypotheses in the censored exponential regression model in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic under a null hypothesis and the corresponding reference chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in the class of censored exponential regression models. A Bartlett-type correction for the gradient test is derived in this paper in this class of models. Additionally, we also propose bootstrap-based inferential improvements to the four tests mentioned. We numerically compare the tests through extensive Monte Carlo simulation experiments. The numerical results reveal that the corrected and bootstrapped tests exhibit type I error probability closer to the chosen nominal level with virtually no power loss. We also present an empirical application for illustrative purposes.