Self-consistent estimation of censored quantile regression

The principle of self-consistency has been employed to estimate regression quantile with randomly censored response. The asymptotic studies for this type of approach was established only recently, partly due to the complex forms of the current self-consistent estimators of censored regression quantiles. Of interest, how the self-consistent estimation of censored regression quantiles is connected to the alternative martingale-based approach still remains uncovered. In this paper, we propose a new formulation of self-consistent censored regression quantiles based on stochastic integral equations. The proposed representation of censored regression quantiles entails a clearly defined estimation procedure. More importantly, it greatly simplifies the theoretical investigations. We establish the large sample equivalence between the proposed self-consistent estimators and the existing estimator derived from martingale-based estimating equations. The connection between the new self-consistent estimation approach and the available self-consistent algorithms is also elaborated.