Parametric estimation and robust inference for current status data with Lindley lifetimes

Current status data appear in many biomedical studies when we only know if an event of interest occurs before or after a specific time point. In this paper, we develop statistical inference for the estimation of parameters from current status data under the Lindley lifetime distribution, which is seen to work better than the exponential distribution in some lifetime contexts. We first develop an EM algorithm for Maximum Likelihood (ML) estimation and derive the asymptotic confidence intervals for model parameters. Then, we address the problem of model misspecification and define a new family of robust divergence-based estimators as a robust alternative to ML. Finally, we illustrate these methods through a simulation study as well as a numerical example.