Parameter Estimation And Inference For Regression Models With Censored Data

Censored data is a common complex data type in modern statistical practice.In survival analysis,due to the limitations of experimental design,observation time and other factors,the data collected can not be fully observed.In recent years,the research of statistical analysis method with censored data is an international hot top-ic.Censored data also appears frequently in biomedicine,psychology,sociology,economy and many other applied fields.Quantile regression can more specifically describe the relationship between response variables and covariates.Especially when we focus on some upper and lower quantiles,it becomes a powerful complement to least squares regression.It has a wide range of applications in economics,survival analysis,microbial research and other fields.Estimation and asymptotic properties of various quantile regression models has also been extensively studied.At the same time,empirical likelihood has become a very useful statistical inference tool.Many scholars have applied it to linear model,non-parametric model,semiparametric model and some models under complex data.In this paper,we compare the efficiency of several different methods for esti-mating the censored quantile regression,and studied the problem of parameter esti-mation in quantile regression model with censored data,and the empirical likelihood and asymptotic properties of the parameters are proposed.Firstly,this paper mainly considers the quantile regression model with censored data,compares the efficien-cy of three censored quantile regression methods in parameter estimation.Based on Zhou's censored median regression estimation method,a new method of estimating quantile regression parameters under censored data is proposed and its asymptotic properties are given.Based on the proposed quantile regression parameter estimation method,the corresponding empirical likelihood inference is proposed,and the corre-sponding asymptotic properties are given.Moreover,the asymptotic properties of the proposed method are given.Finally,the effectiveness of the proposed quantile regres-sion estimation method and empirical likelihood method is verified by simulation,and compared with the existing estimation methods,it shows that the proposed estimation method is fast and reliable.