自适应设计广义线性模型下基于Lγ惩罚的变量选择及其渐近理论

Variable Selection and Its Asymptotic Theory Based on LγPenalty in Generalized Linear Models with Adaptive Designs

本文利用Frank和Friedman[3]提出的Lγ惩罚方法,研究了自适应设计广义线性模型下基于惩罚拟似然的变量选择问题及其渐近性质,该方法可同时进行参数估计和变量选择.当0<γ<1时,在适当条件下,本文证明了自适应广义线性模型下基于Lγ惩罚和拟似然的估计量的存在性、相合性和Oracle性质,该结果将广义线性模下固定设计的相关理论推广到了自适应设计情况.最后,本文通过数值模拟和实际数据分析验证所获得理论的有效性.

In this paper,Lγpenalty method proposed by Frank and Friedman[3]is used to study the variable selection problem and its asymptotic properties based on the penalized quasi-likelihood method in generalized linear models with adaptive designs.This method can perform parameter estimation and variable selection simultaneously.For 0<γ<1,the existence,consistency and Oracle properties of the estimators based on Lγpenalty and the quasi-likelihood method in generalized linear models with adaptive designs are proved under appropriate conditions.These results generalize the related theories of generalized linear models from the case of fixed designs to the case of adaptive designs.The validity of our obtained theory is verified by numerical simulation and real data analysis in this paper.