Bayesian Quantile Regression Based On Bi-level Penalty Function And Its Application

With the increase of data volume,the method of variable selection becomes more and more important.In social survey,classification variables often appear,and they often need to be converted into dummy variables in the model,which naturally leads to dummy variable groups.In addition,there may exist other types of variable group structures.Under this situation,group variable selection is more situable than sinlge variable selection method.However,in the era of big data,data value density is low and sparse,so scholars often need to select in-group variables while selecting group variables.Besause quantile regression model is more robust than traditional linear model,this paper decides to combine Sparse Group Lasso and adaptive Sparse Group Lasso which can choose group varaibles and in-group variables at the same time with the bayesian regularization quantile regression model,and proposes BQR.SGL and BQR.adSGL model.And by assigning appropriate prior distributions to the parameters,the posterior distribution of each parameter is deduced and Gibbs sampling is constructed.In order to verify the effectiveness of the model,this paper compares BQR,BQR.GL,BQR.SGL and BQR.adSGL model under various conditions.In the simulation,this paper considers the sparsity of coefficients between and within different groups.The results show that when the sparsity within group becomes larger,the improvement of BQR.SGL and BQR.adSGL on BQR.GL is better,and in most cases,the prediction effect of BQR.adSGL is better than BQR.SGL.Also,this paper explores the estimation effects of the BQR.SGL and BQR.adSGL models under different disturbance terms and sample sizes.The results show that the two models can also achieve good estimation results even under non-ALD disturbance terms.In addition,this paper applies the BQR.SGL and BQR.adSGL models to birth weight data.The main conclusions drawn are:the mother’s smoking can reduce the weight of the child,and this negative effect increases with the increase of the quantile;the mother’s history of hypertension and uterine allergy will reduce the baby’s weight,and this effect is in the low quantile more noticeable.