Fisher Information Matrices with Censoring, Truncation, and Explanatory Variables

This paper shows how to compute the Fisher information matrix and the asymptotic covariance matrix for maximum likelihood estimators for a wide class of parametric models that include combinations of censoring, truncation, and explanatory variables. Although the models are based on underlying location-scale distributions, applications extend, for example, directly to the closely related and widely used Weibull and lognormal distributions. This paper unifies and generalizes a number of previously published results. The results are important for determining needed sample sizes and for otherwise planning statistical studies, especially in the areas of reliability and survival analysis where censoring and/or truncation are generally encountered.