广义线性模型的补偿Lq似然估计

Penalized Lq-likelihood estimators in generalized linear models

考虑以下的广义线性模型(GLM)y_(i)=h(x^(T)_(i)β)+e_(i),i=1,2,…,n,其中h(·)是连续可微函数,{e_(i)}是具有零均值和已知方差σ^(2)的独立同分布随机变量。在线性回归模型的补偿Lq似然方法的基础上,将该方法应用于广义线性模型之中,并研究了补偿Lq似然估计(PLqE)的Oracle性质。仿真结果验证了该方法的有效性,说明了PLqE是稳健的,而补偿最大似然估计(PMLE)则没有稳健性。

In the following generalized linear regression model(GLM)y_(i)=h(x^(T)_(i)β)+e_(i),i=1,2,…,n,where h(·)is a continuous differentiable function,and{e_(i)}is an independent identically distributed(i.i.d.)random variables with zero mean and known varianceσ^(2).Based on this,this paper applied the penalized Lq-likelihood method to the generalized linear regression model,and investigate Oracle properties of penalized Lq-likelihood estimators.Simulation results verified the validity of this approach and showed that the PLqE is robust,while the PMLE is not.