基于经验欧氏似然的线性回归模型变点检测  

On Linear Regression Model Change-point Detection based on Empirical Euclidean likelihood

作　　者：李智航 马岱君 LI Zhi-hang;MA Dai-jun(College of Mathematics and Statistics,Guangxi Normal University,Guilin 541004,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541004

出　　处：《广西民族大学学报（自然科学版）》2020年第1期62-69,共8页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：国家自然科学基金(11861017).

摘　　要：基于截断的经验欧氏似然比对线性回归模型中的系数变点进行检验与估计.首先建立线性回归系数变点模型,根据其特点构造截断的经验欧氏似然比检验函数,证明在零假设下,该检验统计量的极限分布与经典参数对数似然比检验统计量的极限分布相同,利用此极限分布对变点存在与否做出诊断,若变点存在,则给出变点位置的估计,并证明在一定条件下,该估计是具有相合性的,数值模拟结果以及实例分析表明文中提出的方法具有有效性和实用性.Linear regression model has been widely used in various fields.The empirical euclidean method is proposed to detect coefficient change-point in linear regression model.The trimmed empirical euclidean ratio test function is structured depend on the characteristics of coefficient change-point linear regression model.The limits distribution of test statistic under null hypothesis is proved to as same as that with classical parametric likelihood.The change-point detection is made.If the change-point is exists,it’s estimator is given.The estimator is proved to be consistent under some mild conditions.The simulation result and the analysis of real example show that our proposed method is effectiveness and practicality.

关 键 词：线性回归模型 变点 经验欧氏似然 

分 类 号：O212.1[理学—概率论与数理统计]