Semi-parametric MLE in Simple Linear Regression Analysis with Interval-Censored Data

Abstract

Consider the model Y=β X+ε with interval-censored data, where ε has an unknown c.d.f. F_o . 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.

Keywords:

• Bootstrap
• Generalized likelihood
• Iterative algorithm
• Consistency
• AMS 1991 Subject Classification: Primary 62 J05
• Secondary 62 G05

Acknowledgment

Both authors are partially supported by DAMD17-99-I-9390 and DAMD17-00-1-0448.