Research On Improved Elastic Net Penalty Estimatio

Elastic net is a popular and effective regularization method for solving the parameter estimation and variable selection in statistical models,but it does not have oracle properties,adaptive grouping effect and group sparsity,etc.In addition,it has not used the additional useful information of variables to estimate parameters,such as covariance,correlation,specific location and identity information.To address these deficiencies,we propose two improved elastic net estimation methods as follows.Firstly,A weighted ridge-net is proposed by giving the parameters Lasso and Ridge penalties with variable correlations,which utilizes the correlation of the variables to estimate the parameters and has oracle properties,adaptive grouping effect and Bayesian prior.Meanwhile,a simulation study and example analysis were performed based on the Logistic regression model.The results show that the weighted ridge-net has the ability to solve the shortage of elastic net and excellent practicability,this ability and practicability are not lower than or even higher than the two improved methods of elastic net,i.e.,adaptive elastic net and partly adaptive elastic net.Secondly,by combining Adaptive group lasso and Adaptive ridge,an estimation which can solve the shortage of the elastic net on group sparsity,i.e.,the dual adaptive group elastic net is constructed,and proves the consistency,oracle properties and group sparsity of the obtained estimation.Meanwhile,the group sparseness effect of the dual adaptive group elastic net on the Logistic regression model was evaluated by simulation and Birthwt data,respectively.The results show that the group sparseness ability of the dual adaptive group elastic net is not inferior to or even better than that of some group punishment methods with elastic net structure,such as Sparse-group lasso,Gren and Group-adaptive elastic net.