Varying Coefficients In Composite Quantile Regression And Variable Selection

In statistical studies,data and models are two indispensable parts,it is a very critical issue whether a model can perfectly reflect the real information of the data.Therefore,the study about the model has been widely concerned by scholars.The key is whether the model can reflect the majority of important information in the data,whether it can fundamentally solve the problem that researchers want,and whether it can be applied to real life.How to deal with this situation is a worthy work.The paper proposes a varying coefficient model in composite quantile regression,and makes variable selection at the same time.In this way,it not only simplifies the complex relationship between the variables,but also can describe the dynamic changes of the coefficient.In this paper,by adding the penalty function to the objective function,we use the B-spline function to estimate the coefficients in the framework of the variable coefficient model.At the same time,we make the variable selection from the perspective of the group to get the covariates which related to response variable,and their corresponding coefficients.The model structure estimated by data does not make any preconditions in advance,and it combines the flexibility of the varying coefficient model and the efficiency of the composite quantile regression,which provides advice and assistance to the subsequent modeling and decision-making.We make simulation and do case analysis to compare the results of coefficient estimation and variable selection in composite quantile regression,quantile regression and least squares regression.In the simulation study,we mainly find that the composite quantile regression is more stable than the other two models when the error faces different distribution,which means the bias is at a relatively low level and correct selection rate is higher relatively.In the face of high dimensional,these three models are not ideal,but the composite quantile regression is relatively better.To demonstrate this method for practical economic problems have good explanatory,this paper selected Boston housing prices data as this method application example.And the result is tested by simultaneous confidence band.The composite quantile regression can well explain the change of Boston housing prices,and can reflect the real phenomenon of society.