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June 2014 Nonparametric maximum likelihood approach to multiple change-point problems
Changliang Zou, Guosheng Yin, Long Feng, Zhaojun Wang
Ann. Statist. 42(3): 970-1002 (June 2014). DOI: 10.1214/14-AOS1210

Abstract

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.

Citation

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Changliang Zou. Guosheng Yin. Long Feng. Zhaojun Wang. "Nonparametric maximum likelihood approach to multiple change-point problems." Ann. Statist. 42 (3) 970 - 1002, June 2014. https://doi.org/10.1214/14-AOS1210

Information

Published: June 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1305.62158
MathSciNet: MR3210993
Digital Object Identifier: 10.1214/14-AOS1210

Subjects:
Primary: 62G05
Secondary: 62G20

Keywords: BIC , Change-point estimation , Cramér–von Mises statistic , dynamic programming , Empirical distribution function , Goodness-of-fit test

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • June 2014
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