Nonparametric Maximum Likelihood Approach to Multiple Change-point Problems

论文题目：Nonparametric Maximum Likelihood Approach to Multiple Change-point Problems

论文作者：Changliang Zou, Guosheng Yin, Long Feng, Zhaojun Wang

发表杂志：The Annals of Statistics 2014, Vol. 42, No. 3, 970–1002

文章介绍：

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.

所属实验室或研究中心：教育部核心数学与组合数学重点实验室

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