Multiple Imputation For Partial Linear Model With Censored Data And Its Application Based On Quantile Regression

Partial linear model combines the advantages of linear model and nonlinear model,having stronger adaptability and better explanation,so it is widely applied in clinical trials,biomedical,environmental monitoring and economic research.Some statistical inference method applicable to the complete data set may cause great error owing to the universial existence of censored data which has a serious impact on the effectiveness of the model.Therefore,we present a new multiple imputation method for the partially linear model with censored data.Without any assumptions on the distribution of the model,the multiple imputation method we proposed based on quantile regression techniques,the fitted value of the censored variable is selected by the censored probability as its censored quantile in the quantile regression.The final imputation value is based on the multiple imputation method,screening of existing imputation value to determine the most proper values.We can use the common analysis methods of complete data sets to deal with the data sets after multiple imputation.We estimate the coefficients and the linear part and the function of nonlinear part model of the partially linear models based on the M regression.The effectiveness and stability of the proposed method can be verified by the numerical simulation,which make a the comparison with existing estimation methods of partial linear model with censored data.Finally,the proposed method is applied to the environmental pollution data,established the partial linear model and analied the relationship between the response variable,hourly values of the of the concentration of PM 10,and the relevant variables,we give some corresponding suggestions in the end.