Empirical Likelihood Inference For Quantiles Regression With Data Censored

Quantile regression models have been widely used in biology, architecture, economics and clinical medicine, because of better robustness of quantile regression model in the presence of heteroscedasticity and outliers in the data of the case. In practical application, to obtain numerical observation or measurement of incomplete situation is more common. Quantile regression model is mainly to study the relationship between the independent variables and the conditional quantile of the dependent variable. In this paper, we mainly discuss the empirical likelihood inference in the quantile regression model with censored data.First of all, the statement in the first two chapters focuses on the related research status at home and abroad and some preliminary knowledge, definitions of quantile regression and empirical likelihood given. Then, the third chapter discusses the estimation method with censored data is divided into quantiles regression models, and the corresponding asymptotic theory. Then, in the fourth chapter, the first use of jackknife smooth empirical likelihood method for the quantile regression model with censored data, and construct the confidence intervals. Finally, a simulation experiment was carried out in the fifth chapter, the empirical likelihood method is used to construction confidence intervals and obtained coverage and normal approximation confidence intervals and the coverage rate of construction method are compared.In this paper, the Kaplan-Meier weight estimation method and the empirical likelihood estimation method are used to estimate the unknown parameters in the model. Taking smooth empirical likelihood method and(jackknife empirical likelihood method based, by utilizing a combination of smooth processing to identify outliers, correct inconsistencies in the data, more fully using the data information of the SEL(i.e. the smooth empirical likelihood method) and for small samples have good properties of JEL(i.e. jackknife empirical likelihood method). EL(i.e. the empirical likelihood method) to make the following improvements: Firstly, according to the JEL and SEL method and the method of quantile regression model of location parameter is applied SJEL(smooth jackknife empirical likelihood method) to calculate the empirical likelihood ratio statistic. Then, the parameter confidence interval is constructed to deduce the parameters. The main process is the empirical likelihood method by jackknife on the application of a standard sample mean, empirical likelihood ratio statistic can be computed by solving single equation, this process is simple and easy to implement.Simulation results show that in the finite sample case, Empirical likelihood method(EL) has a better coverage and confidence interval than the normal approximation method(NA). Smooth empirical likelihood method(SEL) to construct confidence intervals in the case of small samples is more accurate. And smooth jackknife empirical likelihood method(SJEL) than the traditional empirical likelihood method(EL) in a higher censored rate, there is a better advantage.