Quantile Regression Estimation Of Partially Varying-coefficient Linear Model With Right Censored Data

Censored data is a kind of data that is truncated for some reasons,which is particularly common in survival analysis.Research on the treatment of censored data in survival analysis is a long-term concern of statisticians.This paper studies the quantile regression estimation and the composite quantile regression estimation of partially varying-coefficient linear model by using the three-stage estimation method with right censored data.This paper uses the local polynomial method to expand the varying-coefficient part linearly,and obtains the preliminary estimated values of the linear part and the varyingcoefficient part of the model through quantile regression estimation and composite quantile regression estimation.Then the estimated value of the varying-coefficient part is substituted into the model to obtain the second estimated value of the linear part.Finally,the parameter values of the linear part obtained by the second estimation are substituted into the model to obtain the final estimated value of the varying-coefficient part.In this paper,the asymptotic normality of the estimation results at each step is obtained and the proof process is given.Then in the numerical simulation,the Monte Carlo simulation is used to verify the effectiveness of the three-stage quantile regression estimation method with finite samples.Measure the effect of estimation by calculating the bias of the parameter estimation and the mean square error of the non-parametric estimation of the estimation method at each stage with different censored ratios and error distributions.Finally,the conclusions obtained in the numerical simulation were verified through GBSG2 and Cancer survival data sets in the R software.It is found that the results of the estimation method proposed in this paper in the actual data sets application are consistent with the results of the numerical simulation,which indicated that the estimation method proposed in this paper was effective in the actual data meeting the requirements of the model.