The Partially Linear Varying Coefficient Models Based On Support Vector Weighted Quantile Regression

Compared with the varying coefficient model,the partially linear varying coefficient model has both non-parametric and parametric parts.Making full use of the known prior information can greatly improve the efficiency of the model.Its obvious advantages lie in the form of the model and the interpretation of the regression coefficient.Therefore,statistics,medicine,economics and other fields pay more and more attention to partially linear varying coefficient model.In recent years,scholars at home and abroad have paid most attention to the application conditions of partially linear varying coefficient models,estimation of unknown parameters,prediction and fitting of models,etc.The most critical problem is how to estimate and infer unknown parameters in models.For parameter estimation of partially linear varying function,the most commonly used estimation methods are local polynomial and smooth spline.These two estimation methods based on the least square method are extremely sensitive to outliers and their efficiency will decrease as the error moves away from the normal distribution.Support vector quantile regression is a non-parametric method,which has been widely used in statistical inference since Takeuci(2004)proposed it.It does not need to make any parameter assumption on the distribution function of the data.This method can give full play to the nonlinear processing ability of support vector machines and the quantile regression ability to completely depict the conditional distribution characteristics,and can guarantee high robustness.However,it is difficult to choose the quantile points of this method,and the predicted values of some quantile points may be too far to the right or left.Therefore,this paper considers using the support vector weighted quantile regression method,which can consider multiple quantile points at the same time and make use of more effective information.In this paper,the parameter estimation of partially linear varying coefficient model based on support vector weighted quantile regression is transformed into weighted least-squares problem,which is solved by iterative least-squares and quadratic programming.In order to verify the correctness of the theoretical results and the feasibility of the method,random simulation was carried out.The basic framework of the paper is as follows:In chapter 1,the research background and significance of this paper are introduced.Then the partially linear varying coefficient model and support vector weighted quantile regression method are systematically introduced by combing the related literatures at home and abroad.Finally,the paper summarizes the research content,innovation and key points.In chapter 2,the parameter estimation and inference of partially linear varying coefficient model based on support vector weighted quantile regression are studied.Firstly,the parameter estimation of support vector quantile regression is briefly summarized.Secondly,the partially linear varying coefficient model based on weighted quantile regression of support vector is deduced,and the optimization problem is finally transformed into weighted least squares solution.Then,the weighted least-squares problem is solved by iterative weighted least-squares and quadratic programming respectively.According to methods similar to Bradic(2011),the optimal weight is obtained.Finally,the asymptotic distribution of partially linear varying estimation and its related theorems are proved.In chapter 3,the feasibility of the support vector weighted quantile regression method combined with partially linear varying coefficient model is tested by numerical simulation and case analysis.First,numerical simulation was designed to test the feasibility and rationality of some variable coefficient models and two parameter estimation methods,and then the factors affecting CD4 cell count of AIDS were analyzed by this method.In chapter 4,the paper summarizes the whole paper,and forecasts the future research and development trend of partially linear varying coefficient model based on support vector weighted quantile regression.