基于跳信息准则的均值变点检测  

Mean Change Point Detection Based on Jump Information Criterion

作　　者：张婉瑶 夏志明 ZHANG Wanyao;XIA Zhiming(School of Mathematics,Northwest University,Xi'an,710127,China)

机构地区：[1]西北大学数学学院,西安710127

出　　处：《应用概率统计》2024年第3期409-419,共11页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11771353,12171391)资助.

摘　　要：变点模型已被证实在许多领域具有现实意义,其中均值单变点模型是变点模型的基础.本文主要集中解决单变点统计模型中变点是否存在的统计推断问题.针对均值单变点模型,本文将传统的假设检验思路转化为对变点个数为0个或1个的估计问题,从而避开临界值选择问题;建立了基于跳信息准则的优化目标函数,同时证明了变点个数的相合性及其收敛速度,最后导出最优的跳信息准则的构造形式.数值实验结果表明,我们提出的方法相较于已有的基于检验的方法,具有优异的统计表现.The change-point model has been proved to have practical significance in many fields,in which the mean single change-point model is the basis of the change-point model.This paper mainly focuses on solving the statistical inference problem of whether there is a change point in a single change-point statistical model.For the mean single change-point model,this paper converts the traditional hypothesis testing idea into an estimation problem for the number of variable points to be 0 or 1,thus avoiding the critical value selection problem;the optimization objective function based on the jump information criterion is established,and the consistency of the number of change points and its conver-gence speed are proved,and finally the construction form of the optimal jump information criterion is derived.The numerical experimental results show that our proposed method has superior statistical per-formance compared to existing test-based methods.

关 键 词：均值单变点模型 跳信息准则 惩罚项 相合性 

分 类 号：O212.1[理学—概率论与数理统计]