| n this dissertation, we consider estimation in two important regression models, the linear regression model with unknown error distribution and the Cox's proportional hazard model, with interval censored data.;In the first part of this dissertation, several estimation procedures are proposed for a linear regression model under interval censoring. The first two estimators are natural extensions of the estimators proposed for the binary choice model in the econometrics literature: these include the maximum scored likelihood estimator, and the maximum rank correlation estimator. Asymptotic properties of these estimators are studied. However, the major emphasis in the first part is on more efficient estimators based on the likelihood function, including generalized M-estimators, and estimators based on maximizing the profile likelihood or modifications thereof. Central limit theorems are established for the generalized M-estimators and the modified maximum profile likelihood estimators. The modified maximum profile likelihood estimator is shown to be fully efficient. The consistency of the maximum likelihood estimator is proved.;In the second part of this dissertation, a general theorem on the asymptotic distribution of the maximum likelihood estimator of the finite dimensional parameter in a class of semiparametric models is given. This theorem is then applied to the Cox model under interval censoring. Asymptotic efficiency of the maximum likelihood estimator of the regression parameter is established as an application of the general theorem.;In both the linear regression model and the Cox model, the (iterative) convex minorant algorithm plays an important role in characterizing the maximum profile likelihood estimators of the error distribution F or the baseline cumulative hazard function... |
