Variable Selection For Generalized Linear Model With Adaptive Elastic Net

Generalized linear model is one of very important model in the statistics,it is has been widely used in biological,economic,social,medical and other fields.In the process of modeling,people often consider many independent variables.How to choose the real related variables on the depen-dent variable is concerned in the research of variable selection.So it has strong application value and practical significance to study the variable selection of generalized linear model.In this paper,we use adaptive elastic net estimation method discuss variable selection problem of generalized linear models.First of all,we give adaptive elastic net parameter estimation method under generalized linear model:Then with the aid of this estimation method,we give generalized linear model of variable selection algorithm;Then we give adaptive elastic net estimation method of statistical properties theoretically under the generalized linear model,such as asymptotic nor-mality and weak consistency,sparsity and effect between groups,etc.,Through these properties show that the adaptive elastic net meet the Oracle properties and able to solve the problem of vari-able which has a strong correlation between variables;At last,we conduct some simulations with variable selection methods,Such as bridge regression.Lasso,adaptive Lasso and elastic net esti-mate method.The simulation results show that under the BIC rule,adaptive elastic net estimation method better than other common variable selection method.