LAUSR

An estimation for censored quantile regression models, which is based on an inverse-censoring-probability weighting method, is studied in this paper, and asymptotic distribution of the parameter vector estimator is obtained. Based on the parameter estimation and asymptotic distribution of the estimator, an empirical likelihood inference method is proposed for censored quantile regression models and asymptotic property of empirical likelihood ratio is proved. Since the limiting distribution of the empirical likelihood ratio statistic is a mixture of chi-squared distributions, adjustment methods are also proposed to make the statistic converge to standard chi-squared distribution. The weighting scheme used in the parameter estimation is simple and the loss function is continuous and convex, and therefore, compared with empirical likelihood methods for quantile regression models with completely observed data, the methods proposed in this paper will not increase the computational complexity. This makes it especially useful for data with medium or high dimensional covariates. Simulation studies are developed to illustrate the performance of proposed methods.