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February 2019 Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data
Lynna Chu, Hao Chen
Ann. Statist. 47(1): 382-414 (February 2019). DOI: 10.1214/18-AOS1691


We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information among observations, which can be applied to various data types as long as an informative similarity measure on the sample space can be defined. The existing approach along this line has low power and/or biased estimates for change-points under some common scenarios. We address these problems by considering new tests based on similarity information. Simulation studies show that the new approaches exhibit substantial improvements in detecting and estimating change-points. In addition, under some mild conditions, the new test statistics are asymptotically distribution-free under the null hypothesis of no change. Analytic $p$-value approximations to the significance of the new test statistics for the single change-point alternative and changed interval alternative are derived, making the new approaches easy off-the-shelf tools for large datasets. The new approaches are illustrated in an analysis of New York taxi data.


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Lynna Chu. Hao Chen. "Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data." Ann. Statist. 47 (1) 382 - 414, February 2019.


Received: 1 June 2017; Revised: 1 February 2018; Published: February 2019
First available in Project Euclid: 30 November 2018

zbMATH: 07036205
MathSciNet: MR3910545
Digital Object Identifier: 10.1214/18-AOS1691

Primary: 62G32
Secondary: 60K35

Keywords: Change-point , graph-based tests , High-dimensional data , network data , non-Euclidean data , nonparametric , scan statistic , tail probability

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.47 • No. 1 • February 2019
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