含MA误差的线性模型的经验似然推断  

Empirical Likelihood Inference for Linear Models with MA Errors

作　　者：蒙海珍 张正家 秦永松 MENG Haizhen;ZHANG Zhengjia;QIN Yongsong(School of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2023年第3期144-154,共11页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(12061017,12161009);广西高校中青年教师科研基础能力提升项目(2022KY0049);广西师范大学数学与统计学院研究生创新计划项目(YJSCXP202106)。

摘　　要：采用拟极大似然估计方法获得含MA误差的线性模型估计方程。为了能够使用经验似然方法,先利用鞅差序列将估计方程中的二次型转化为线性形式;再构造关于模型参数的经验似然比统计量,在一定假设条件下证明该统计量渐近服从卡方分布;模拟结果表明,在参数置信域的覆盖率方面,经验似然方法比参数似然方法更接近置信水平。In this paper,the quasi maximum likelihood estimation method is used to obtain the estimation equation of the linear model with MA errors.In order to use the empirical likelihood method,the quadratic form in the estimation equation is transformed into a linear form of a martingale difference array,and then the empirical likelihood ratio statistics of the model parameters are constructed.Under certain assumptions,it is proved that the statistics asymptotically obey the chi-square distribution.Finally,the simulation resucts show that the empirical likehood method is closer to the confidence level than the parametric likehood method in terms of the coverage of confidence region.

关 键 词：线性模型 MA模型 鞅差序列 经验似然 

分 类 号：O212.7[理学—概率论与数理统计]