Double Sparse Quantile Regression Incorporating Graphical Structure Among Predictors

With the development of science and technology,high-dimensional data,especially heterogeneous high-dimensional data,such as genetic data,economic data,and tomography data,have become more and more common.The graph structure information of prediction variables can effectively improve the performance of the model in parameter estimation,variable selection and prediction accuracy.Regularized quartile regression model is commonly used to deal with high dimensional heterogeneous data.In this paper,we consider a point-to-point method to establish a regularized fractal regression model by using the structure information of the graph of predictive variables,and propose a double sparse high dimensional fractal regression model based on the structure of the graph of predictive variables.The problems of model solving,parameter estimation and variable selection are studied systematically.Under relatively general conditions,it is proved that the proposed method has the consistency of model selection,model estimation and oracle property.A modified alternate multiplier method(ADMM)is used to solve the model,and the convergence of the algorithm is proved.The results of simulation and actual data show that the proposed method has certain advantages in the estimation accuracy and prediction ability.