Asymptotic Properties Of Adaptive LASSO Penalized Least Squares For Adaptive Generalized Linear Models

Generalized linear model is a kind of widely used statistical model.Since the generalized linear model was put forward,it has been concerned by statisticians and practical workers,and The problem of variable selection in generalized linear model is one of the hot issues.The traditional variable selection methods mainly include optimal subset regression method and stepwise regression method,but they lack stability.In recent years,statisticians have proposed variable selection methods such as Lasso,Scad and adaptive Lasso,which mainly focus on the generalized linear models with fixed design,while there are few researches on the generalized linear models with adaptive design.In this paper,the adaptive Lasso method is applied to the generalized linear models with adaptive design.The specific contents are arranged as follows: The first chapter mainly introduces the research background of this topic and the research status of this kind of problem at home and abroad.The second chapter mainly introduces the basic knowledge needed in this paper.The third chapter introduces the main conclusions and numerical simulation results.In chapter four,the consistency and Oracle properties of adaptive Lasso estimators in adaptive generalized linear models are proved.The fifth chapter is the summary of this article and looking to the future research.The appendix gives the detailed results of the data simulation.In this paper,we extend the variable selection problem of the fixed design generalized linear model to the adaptive design,combine the adaptive Lasso method and the nonlinear least squares method,and prove that the method has Oracle property under certain conditions.This method can realize variable selection at the same time of parameter estimation,This is the main work and innovation of this paper.