Semiparametric EM-estimation of censored linear regression models for durations

Abstract

This paper investigates the sensitivity of maximum quasi likelihood estimators of the covariate effects in duration models in the presence of misspecification due to neglected heterogeneity or misspecification of the hazard function. We consider linear models for r(T) where T is duration and r is a known, strictly increasing function. This class of models is also referred to as location-scale models. In the absence of censoring, Gould and Lawless (1988) have shown that maximum likelihood estimators of the regression parameters are consistent and asymptotically normally distributed under the assumption that the location-scale structure of the model is of the correct form. In the presence of censoring, however, model misspecification leads to inconsistent estimates of the regression coefficients for most of the censoring mechanisms that are widely used in practice. We propose a semiparametric EM-estimator, following ideas of Ritov (1990), and Buckley and James (1979). This estimator is robust against misspecification and is highly recommended if there is heavy censoring and if there may be specification errors. We present the results of simulation experiments illustrating the performance of the proposed estimator.