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

作　　者：朱春华[1] 单苗慧 高启兵[2] Zhu Chunhua;Shan Miaohui;Gao Qibing(School of Statistics and Data Science,Nanjing Audit University,Nanjing,211815,China;School of Mathematical Sciences,Nanjing Normal University,Nanjing,210046,China)

机构地区：[1]南京审计大学统计与数据科学学院,江苏南京211815 [2]南京师范大学数学科学学院,江苏南京210046

出　　处：《南京师大学报（自然科学版）》2024年第1期7-13,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家社科基金项目(21BTJ030).

摘　　要：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.

关 键 词：多元广义线性模型 广义估计方程 经验似然 置信域 

分 类 号：O212.4[理学—概率论与数理统计]