The Lasso And Its Methods Of Model Selection In Generalized Linear Models

Model selection is an extremely important part of the statistical modeling . The traditional methods which generally use stepwise regression with AIC and BIC criteria for the choice of the optimal model exsit some limitaions. Tibshirani, R. (1996) proposed a new model selection method called Lasso which overcome the limitaions. Efron, etc. (2004) proposed that an effective algorithm to solve Lasso. There are also some limitaions in Lasso method.Many scholars put forword the improved Lasso methods, such as:SCAD(Fan 2001 ),Adaptive lasso (Zou 2006 and Wang 2007),elastic net (Zou and Hastie 2005) and Relaxed Lasso (Nicolai Meinshausen 2007).The main job of this paper are following:(1) We give a comprehensive comparative study of Lasso,SCAD,Adaptive-lasso,elastic net and Relaxed Lasso based on linear model and point out the relationship of them.(2) We study Lasso and related methods of some differences in Logistic regression methods used the real data ,and systemetically introduce the unified approach to Lasso model selection on the basis of generalized linear model.(3) Finally, we point out some problems to further study.