Non-parametric maximum likelihood estimation of censored regression models

This paper presents a consistent estimator of a censored linear regression model which does not require knowledge of the distribution of the error term. The estimator considered here applies Duncan's (1982) suggestion that the likelihood function for the censored regression model be treated as a functional of both the unknown regression vector and the unknown error distribution. Our estimator is the majorizing regression vector for this non-parametric likelihood functional. We find conditions which ensure the consistency of the NPMLE. The paper concludes with the results of Monte Carlo experiments which show the NPMLE to be more efficient than Powell's Least Absolute Deviations (LAD) estimator, particularly when the fraction of censored observations is large and the sample size is small.