As direct generalization of the quantile regression for complete observed data, an estimation method for quantile regression models with interval censored data is proposed, and the property of consistency is obtained. The property of asymptotic normality is also established with a bias converging to zero, and to reduce the bias, two bias correction methods are proposed. Methods proposed in this paper do not require the censoring vectors to be identically distributed, and can be applied to models with various covariates. Simulation results show that the proposed methods work well.

A variable selection procedure based on least absolute deviation (LAD) estimation and adaptive lasso (LAD-Lasso for short) is proposed for median regression models with doubly censored data. The proposed procedure can select significant variables and estimate the parameters simultaneously, and the resulting estimators enjoy the oracle property. Simulation results show that the proposed method works well.

Least absolute deviations (LAD) estimator for multiple regression models with doubly censored data is proposed and the asymptotic normality of the estimator is established. The proposed method doesn't require the censoring vectors to be identically distributed and the estimator can be applied to models with either fixed or random design. Moreover, as a generalization of the LAD estimator for models with complete observed data, the proposed estimator is robust to heteroscedasticity of the errors.

Varying coefficient models have been studied for many years, and local kernel estimation is an important method to estimate the coefficient functions. Since same bandwidth parameter is used for each coefficient function, local kernel estimation is not effective when the degree of smoothness is different for each coefficient function. In this paper, a new global estimation method based on kernel function and backfitting is proposed. In this method, different bandwidth parameters can be used for each coefficient function to improve the estimation accuracy, and asymptotic properties of the estimators are proved. To reduce the computational complexity, an adaptive global estimation method, which is based on an estimation of the bandwidth ratio and has only one bandwidth parameter to be selected, is proposed. Simulation results show that the proposed methods work well, and two real data examples further demonstrate the potential of the proposed methods.

Recently, least absolute deviations (LAD) estimator for median regression models with doubly censored data was proposed and the asymptotic normality of the estimator was established. However, it is invalid to make inference on the regression parameter vectors, because the asymptotic covariance matrices are difficult to estimate reliably since they involve conditional densities of error terms. In this article, three methods, which are based on bootstrap, random weighting, and empirical likelihood, respectively, and do not require density estimation, are proposed for making inference for the doubly censored median regression models. Simulations are also done to assess the performance of the proposed methods.