Research On Variable Selection Of Multiplicative Regression Model

Variable selection problem of the model is a hot research topic in modern statis-tics.Scholars have done a lot of work,especially the research on LASSO and its re-lated methods.There are more commonly used methods:LASSO、Fused LASSO、Adaptive LASSO、SCAD、Elastic Net、Adaptive Elastic N et、L₂—Fused LAS SO etc.In addition,in the theoretical study,applied the most are the linear regression model.But it has not been used in such as stock price,the survival time etc data types in real life,because these data types are negative.Multiplicative regression model can well deal with this kind of data,which is more applied to practical problems.But there are few research results about variable selection methods in multiplicative regression model.So,in this paper,we will study the problem of variable selection methods in the multiplicative regression model.In this paper,we will use the multiplicative regression model.On one hand,we will extend the Adaptive LASSO、Adaptive Elastic Net and SCAD methods to multiplica-tive regression model,research on the variable selection problem of the multiplicative regression model,and get these three methods all have oracle property based on LPRE criterion;On the other hand,we will put forward a new method of variable selection,that is the Adaptive L₂--Fused LASSO method,and get it also has oracle property based on LPRE criterion.In this paper,we will not only theoretically prove that the above four methods all have oracle property,but also from the aspects of the numerical simulation shows that the implementation of the above four methods in variable selection of multiplicative regression model.