Efficient sieve estimation of semiparametric probit model with doubly censored data

Semiparametric probit model serves as a valuable alternative to the popular proportional hazards/odds model in survival analysis partly due to the use of a standard normal distributed random error. This feature can facilitate developing an efficient inference and may render a better fit for the real world data than other models. In this work, we concern regression analysis of doubly censored data with a spline-based probit regression model and provide an efficient maximum likelihood estimation procedure. A novel and reliable expectation-maximization algorithm is proposed to identify the sieve estimator. Asymptotic properties of the proposed estimator are established. Simulation studies suggest that the proposed method works well in finite samples and obviously outperforms the direct sieve maximum likelihood method, which is accomplished with some existing optimization algorithm in the software. An application to a real data set is also provided.