Quantile Estimation For Censored Partially Linear Additive Models And Its Application Based On Nonparametric Multiple Imputation

Partially linear additive models are a generalization of multiple linear regression models and nonparametric addtive models.They have the properties of both parametirc models and nonparametric models,but they show better flexibility than the former and are more effective than the latter.Therefore,they are widely applied in many fields of science,such as medicine and biology.However,some statistical inference methods applicable to the complete data sets may cause large deviations owing to the existence of censored data which has a impact on the effectiveness of the model in varying degrees.Therefore,how to deal with censored data effectively has become the focus of scholars in recent years.In this paper,a nonparametric multiple imputation method based on quantile regression is proposed for the partially linear additive model with fixed censored data.This method does not need to make any assumptions about the distribution of the model.We use conditional quantile to estimate the conditional probability density of censored variable,then a distribution sampling is constructed,finally several sets of data are obtained after multiple imputation.In this paper,the coefficients in the linear part and nonlinear functions are estimated based on quantile regression and composite quantile regression respectively with these data sets.Furthermore,we adopt the adaptive LASSO method to select sigificant variables in the linear part.In order to verify the validity of the method we adopted in this paper,the multiple imputation method proposed is compared with the existing estimation methods of censored partially linear additive models by numerical simulation.The results show that the quantile estimation based on multiple imputation method is more effective than the others in the models of normal distribution error term,heavy tail error term and conditional heteroscedastic error term.For the problem of variable selection,the adaptive LASSO method based on the data sets which have been filled can accurately identify the significant variables in the linear part of the model,and obtain the coefficient estimates of the these variables simultaneously.In the example,the proposed estimation method is applied to nutritional epidemiology data,a partially linear additive model is established to analyze the relationship between the plasma concentrations of beta-carotene,and personal characteristics and dietary factors.The result shows that quetelet,whether farily often use vitamin and dietary beta-carotene consumed per day are correlated with plasma concentrations of beta-carotene.Among them,Quetelet is negatively correlated with plasma concentrations of beta-carotene,while remaining variables are positively correlated with that.