Statistical Inference Of Semiparametric Quantile Regression Model With Interval Censored Data

Interval censoring data is naturally generated in many clinical trials and longitudinal studies,in which individuals are tested regularly instead of continuously.For example,when the response variable Y_i is interval censored,only the vector satisfying P(t_1i<Y_i?t_2i)=1 can be observed t_1i and t_2i.Quantile regression is an important research object in statistics.Compared with linear regression,it can describe the entire conditional distribution.The semiparametric quantile regression model combines the advantages of the quantile regression model and the semiparametric estimation method.The semiparametric conditional quantile estimation can take into account the linearity and nonlinearity of the variables,and there is no strict parameter constraint on the relationship between the variables.Therefore,it is very meaningful to study the semiparametric quantile regression model based on interval censored data.This article is mainly divided into the following two parts.The first part mainly studies the varying-coefficient quantile regression model under interval censored data.Based on interval censored data,we propose an estimation method of varying-coefficient quantile regression model.The advantage of this method is that the censored vectors do not need to be identically distributed.This method is based on the expansion of the complete observation data,and the loss function is modified.The estimated value is defined as the optimal solution point of the proposed objective convex function minimization problem.And under certain regularity conditions,the consistency and asymptotic normality of ?_?(T)are given,and the asymptotic normal cooking is given when the deviation converges to zero,and a rigorous proof of the asymptotic property is given.First,give four lemmas and prove them.Through the proof of the lemma,theorem 1(consistency)and theorem 2(asymptotic normality)are further proved.Finally,the effectiveness of the method is verified through some simulation studies and case analysis.We also compared the performance of our proposed method with other methods in the varying-coefficient quantile regression model,and the results show that our proposed estimation method is more superior.The second part mainly studies some linear quantile regression models under interval censored data.Based on interval censored data,the estimation method proposed in the first part is extended to part of the linear quantile regression model.First,the weight function W_nj(t)is used to transform the partial linear function,and then the estimation function of the partial linear quantile regression model is obtained according to the method proposed in the first part.The feasibility of the method is proved by the simulation research under different parameter distributions,and the practicality of the method is further proved by the actual data analysis.