Semi-parametric MLE in simple linear regression analysis with interval-censored data

Consider the model Y = βX + ε with interval-censored data, where ε has an unknown c.d.f. F₀. The semi-parametric MLE (SMLE) of β is well defined, but cannot be obtained by algorithms for M-estimators, or by the Newton-Raphson method or the Monte-Carlo method. Thus it has not been studied in the literature even in the case of complete data. We propose a feasible algorithm to obtain all solutions of the SMLE. Simulation suggests that the SMLE is consistent and the bootstrap estimator of the variance of the SMLE matches the sample variance. We compare the SMLE to the Buckley-James estimator (BJE) in four data sets with sample sizes up to 374. The results show that the SMLE is more robust and more reliable than the BJE.