基于跳信息准则的均值变点检测
Mean Change Point Detection Based on Jump Information Criterion
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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.Abstract: 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 convergence 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 performance compared to existing test-based methods.