线性再生散度模型的极大L_(q)-似然估计的渐近性质  

Asymptotic properties of the maximum L_(q)-likelihood estimates in linear reproductive dispersion models

作　　者：胡宏昌 吴乔艳 HU Hong-chang;WU Qiao-yan(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北师范大学学报（自然科学版）》2023年第4期17-24,共8页Journal of Hubei Normal University：Natural Science

基　　金：湖北师范大学“研究生创新科研”立项建设项目(2023Z080)。

摘　　要：线性再生散度模型是线性回归模型、广义线性模型和指数线性模型的自然推广,极大L_(q)-似然估计是基于非广义熵的新参数估计方法,是极大似然估计的推广。用极大L_(q)-似然估计研究线性再生散度模型,在一定的条件下,给出了线性再生散度模型的极大L_(q)-似然估计的弱相合性和渐近正态性。最后通过模拟算例表明:随着n的增大参数估计值越接近真值;当q→1时,ML_(q)E的参数估计值接近于MLE的参数估计值。Linear reproductive dispersion models(LRDMS)are the natural generalization of linear regression models,generalized linear models and exponential linear models.Maximum L_(q)-likelihood estimator(ML_(q)E)is a new parametric estimator based on nonextensive entropy,which is a generalization of maximum likelihood estimation.In this paper,ML_(q)E is used to study LRDM,the weak consistency and asymptotic normality of ML_(q)E of RDLM are obtained under certain assumptions.Finally,it is illustrated by a simulation example:parametric estimator gets closer to the true value with the increasing of n,and the parametric estimator of ML_(q)E is close to the parameter estimate of MLE.

关 键 词：线性再生散度模型 极大L_(q)-似然估计 存在唯一性 弱相合性 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]