GEE下经验似然估计的渐近正态性质  

The Asymptotic Normality Properties of Empirical Likelihood Estimation Under GEE Model

作　　者：靳永涛 尹长明[1] 吴迪 JIN Yongtao;YIN Changming;WU Di(College of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学数学与信息科学学院

出　　处：《四川理工学院学报（自然科学版）》2019年第6期90-96,共7页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金(11061002);广西自然科学基金(2015GXNSFAA139006)

摘　　要：在较弱的限制条件和不服从独立同分布的情况下,分析含有参数信息的广义估计方程下的经验似然方法。首先给出较易验证的假设条件和正态收敛法则等引理及其证明,其次在较弱条件下给出经验似然估计存在性、相合性和渐近正态分布等的理论验证,结果表明经验似然比LE(β)在条件范围内几乎处处收敛到经验似然比最小值LE(β^)且经验似然估计参数表达式∑n^1/2(β^|-β0)渐近高维正态分布等,使得对于GEE下经验似然估计的相合和渐近正态等性质有了更为准确,更易满足现实模型的理论结果。最后运用R语言运行统计模拟,发现经验似然方法比广义估计方程方法回归拟合度更理想。Under the condition of weak constraints and disobedience to independent and identical distributions, the empirical likelihood method under the genneralized estimation equation containing parameter information is anaiyzed. Firstly, we give the assumptions that can be easily exemplified and lemmas like normal asymptotic principle with their prove. Secondly, the theoretical verification of the existence, consistency, and asymptotic normal distribution of emporocal likelihood estimates under weaker conditions is given. The results show that empirical likelihood ratio function LE(β) almost sure converges to the minimum of empirical likelihood ratio LE(β^) in a given conditions and empirical likelihood estimator ∑n^1/2(β^|-β0) have asymptotic high-dimensional normal distributions, which means it is a more accurate and easier fitted to reality model for empirical likelihood method under GEE. In addition, we also take the statistic simulation for practical purposes that demonstrate the EL method is better than GEE method.

关 键 词：经验似然 广义估计方程 纵向数据 相合性 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]