半参数广义线性模型的惩罚似然估计

THE PENALIZED LIKELIHOOD ESTIMATORS FOR THE SEMIPARAMETRIC GENERALIZED LINEAR MODELS

一、引言我们知道,通常的广义线性模型其联接函数为 g(μ)=η,并且预测η有一已知参数形式,即η=xβ.然而,如果预测依赖于协变量的形式知道的并不很清楚,那么这时采用参数的线性化结构并非总是适当的.当缺乏确切的信息时,有时用非参数方法更可取.但是,当确信某些关系具有一定的参数形式时,完全的非参数方法其效率可能相当低.于是,可以考虑更一般的模型——半参数广义线性模型,它是由 Green 和 Yandell 等一些作者提出来的.这个类包括了通常的广义线性模型及非参数广义线性模型,因而处理问题也就更灵活了.

In this paper,the penalized likelihood estimators of the parameters and nonparametricfunctions for the semi-parametric generalized linear models are discussed.Detailed statementsof the evaluation of the penalized likelihood are given,and the penalized minimum likelihoodestimation is proved to be equivalent to the penalized weighted LSE.Moreover,the Bayesianexplanation of the penalized likelihood estimation is presented and the choice of the smoothingparameter “λ” is discussed.Finally a method of the penalized qusai-likelihood for the SGLMis suggested.