Estimating methods for quantile residual life regression model with censored length-biased data

So far, compared with quantile regression models, there has been relatively little research work done on quantile residual life regression models. The main purpose of this paper is to make statistical inference for quantile residual life regression model with censored length-biased data. Based on the martingale theory, two estimating equations are developed, which can lead to avoid estimating the survival function of the censoring variable, and a two-stage procedure is proposed to calculate the estimates of regression parameters, too. The uniform consistency and weak convergence of proposed estimators are also provided. In addition, results of the simulations show that the proposed composite martingale-based estimating method performs slightly better than the proposed martingale-based one in terms of the empirical standard derivations and empirical mean square errors. Finally, the Channing House data is employed to illustrate their applications.