多元广义线性模型经验似然方法分析

Analysis of Empirical Likelihood Methods for Multivariate Generalized Linear Models

针对多元广义线性模型,基于估计相关阵、广义估计方程和经验似然方法,本文构造出经验似然比统计量,此统计量能克服“工作相关阵”方法的误设定问题.在一定的条件下,本文也获得了经验似然比统计量渐近Wilks性质,该结果可用作未知参数向量置信域的构造.最后,通过数值模拟对所提方法的有效性进行验证.

For the generalized linear models with multivariate responses,based on the estimating correlation matrix,the generalized estimating equations and empirical likelihood methods,this paper constructs the empirical likelihood ratio statistics which can overcome the mistakenly specification caused by the method of“working correlation matrix”.Under certain assumptions,this paper also obtains the asymptotic Wilks property of the empirical likelihood ratio statistics,which can be used to construct the confidence region of the unknown parameter.Last,the validity of the proposed method is verified through the numerical simulations.