Exact Post-Selection Inference And Application In Elastic Net

Nowadays,the data-driven modeling process has become the mainstream trend of statistical data analysis.How to obtain a more realistic and effective model has always been a hot issue that people care about.For linear regression models,as one of the most classic and widely used models,the problem between its model and inference has long been noticed by statisticians.In fact,in the process of model selection,with the lack of consideration about the selection effect including which variable selection method is used,as long as the variable selection process determines a set of selected variables,it will be taken for granted as the "correct"choice.This will lead to the loss of the rationality and authenticity of classical statistical inference theory,so that the goal of measuring the statistical strength of model variables cannot be well achieved.In order to deal with the above problem,statisticians proposed a scheme which takes the selection effect of the selection process on the final selected model in-to account by adjusting the classical statistical inference based on the model selection process {M=M} after model selection.This scheme is so-called Post-Selection Inference.In addition to the theoretical advantages of post-selection inference,there is the possibility of simultaneously solving the problem that the statistical strength of the variables in the calculation model may be difficult to judge in terms of concept and analysis.So far,there have been diverse research results in the field of post-selection inference.Among them,the PoSI method first proposed by Berk et al.in 2013 and the theoretical framework of Exact Post-Selection Inference proposed by Lee et al.in 2016 are two significant representa-tions,which promoted the development of theory and tools in the post-selection inference field.Firstly,this paper systematically expounded two methods of post-selection inference——the PoSI method and the Exact Post-Selection Inference,and com-pared the differences in coverage methods and assumptions between the two.Secondly,this paper applied the theoretical framework of Exact Post-Selection Inference to the linear regression model which used the elastic net to select vari-ables.According to the theoretical framework of Exact Post-Selection Inference,the selection event of the elastic net linear regression model was reconstructed,and the expression of the p-value and the confidence interval of the regression coefficient as the statistic of test obeys the truncated normal distribution was obtained.Last but not least,several data experiments were carried out in this paper to do comparison and study about the exact post-selection inference of the elastic net linear regression model.The innovation of this paper is that it applied the Exact Post-Selection In-ference theory to the elastic net linear regression for the first time.And it not only provides a new theoretical basis and new data examples for improving the elastic net linear regression model in practical applications,but also facilitates the application and promotion of post-selection inference theory and tools.