B-Spline Estimation Of Semi-Parametric Quantile Regression Model With Missing Data And Its Application

Partial linear variable coefficient model,an important semi-parametric regression model,not only retains the advantages of strong adaptability and robust regression of non-parametric model,but also has the characteristics easily interpreting of parametric model.There are not only parametric components but also non-parametric components in the model,reflecting the situation for part of coefficient,changing with the change of variate and closing to realistic data.In reality,data will often be lost due to some uncontrollable factors.If the complete data method is adopted,a large amount of information will be lost,resulting in poor estimation effect.Scholars show inverse probability weighting an effective method,so this method is used to process data with random missing covariates in paper.Quantile regression estimation with a wide application,can make up for the shortcomings of least square estimation,such as sensitivity to outliers and multiple model assumptions.In paper,a method combining B-spline and inverse probability weighting are proposed to estimate the parameters and non-parameters of a partial linear variable coefficient quantile regression model with missing covariates.For estimation process,the logistic model is used to generate the loss probability of covariate random loss firstly,and B-spline approximation technique is used to construct the loss function of inverse probability weighted quantile regression later,using the loss probability of partial linear variable coefficient model to get the estimation of the model's non-parametric function.In the simulation study,three cases,namely the missing probability known,the missing probability estimated by non-parametric method and the missing probability estimated by parametric method,are considered to get the estimation of the non-parametric component and the parameter component.It is found that in the case of covariate random missing,the quantile regression of the partial linear variable coefficient model combining B-spline and inverse probability weighting performs well with limited samples,and the simulation results show that the estimation method is effective.In certain circumstances,the convergence of the non-parametric function part and the asymptotic property of the parametric part are proved as well.Last but not least,the estimation method in the research applies to the ozone and meteorological factors in Chongqing during the whole year of 2019,to study the ozone content's relationship with gas pressure,temperature,sunshine time and humidity,and the relationship among dependent variables is relatively complex.Therefore,respectively from three aspects about linear,nonlinear relations and interaction affect,the effective modeling results can better reflect the regression relationship between ozone content and meteorological factors in Chongqing,and further prove the rationality of the estimation method.