Quantile Regression For Varying-coefficient Linear Model With Censoring Indicators Missing At Random

In our real life,in addition to the need for statistical research on complete data,we are often faced with a large number of deleted and truncated data,which is particularly common in survival analysis.In this thesis,quantile regression estimation of variable coefficient linear model is studied for data with censoring indicators missing at random.In this thesis,the variable coefficients are linearly expanded by the local linear expansion method.For different weighting methods,we construct the calibration estimators and interpolation estimators of the variable coefficients linear model under the quantile regression and compound quantile regression methods,and prove the asymptotic normality under the corresponding assumptions.We also propose a hypothesis testing procedure based on Bootstrap method for the properties of the variable coefficient linear model to verify whether the model conforms to the variable coefficient linear model.Later in the numerical simulation,we through the Monte Carlo method to produce data,because this article need to delete evaluation the absence of the random model to estimate loss,so we need to build the model to simulate the delete loss ratio and loss ratio.The exponential model was constructed to simulate the deletion situation,and the logit model was constructed to simulate the deletion situation.The MSE of each variable coefficient and the overall GMSE of different estimation methods under different censored ratio and missing ratio were calculated,so as to evaluate the effect of the model and test the model checking program.Finally,our estimation method using the actual data,choose the own GBSG2 packets in R language,through the study of the data of breast cancer patients,the conclusion is consistent with the numerical simulation,and it is confirmed that the quantile estimation method is better than the original least square LS method in the estimation of the linear model with variable coefficient under data with censoring indicators missing at random.