Composite Quantile Regression for Partially Linear Additive Model with Censored Responses and Its Application

In this paper, for a widely applicable semi-parametric model, partially linear additive model, we study the estimation of its coefficients and nonparametric functions when responses are censored. For this, a composite quantile regression estimation method based on data augmentation is proposed. This method utilizes the relationship between quantile regression and distribution function to construct the imputation dataset, and the final estimators are obtained by composite quantile regression through iterations. The proposed method relaxes the assumptions of the model, not only has low requirements for initial values of iterations but also allows the case when different types of censoring are present in the same dataset. Numerical simulations show that the proposed method can accurately estimate the coefficients and nonparametric functions of the censored partially linear additive model. In real data analysis, this paper studies the air quality in Beijing, and measures the effects of PM10 concentration, CO concentration, temperature, air pressure, and dew point on PM2.5 concentration. The results show that the composite quantile regression of the partially linear additive model can describe well the influence of these factors on PM2.5 from the perspective of linear and nonlinear relationships, and the proposed method performs well in the processing of censored data.