Covariance matrix of maximum likelihood estimators in censored exponential regression models

Abstract

The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the formula only involves simple operations on matrices and hence is quite suitable for computer implementation. Monte Carlo simulations are provided to show that the second-order covariances can be quite pronounced in small to moderate sample sizes. Additionally, based on the second-order covariance matrix, we propose an alternative Wald statistic to test hypotheses in this class of regression models. Monte Carlo simulation experiments reveal that the alternative Wald test exhibits type I error probability closer to the chosen nominal level. We also present an empirical application for illustrative purposes.