A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data

By David S. Matteson, Nicholas A. James. 2013

609 citations recorded by the source corpus.

Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data are continually arriving and are analyzed adaptively. We are concerned with the related, but distinct, offline version, in which retrospective analysis of an entire sequence is performed. For a set of multivariate observations of arbitrary dimension, we consider nonparametric estimation of both the number of change points and the positions at which they occur. We do not make any assumptions regarding the nature of the change in distribution or any distribution assumptions beyond the existence of the αth absolute moment, for some α ∈ (0, 2). Estimation is based on hierarchical clustering and we propose both divisive and agglomerative algorithms. The divisive method is shown to provide consistent estimates of both the number and the location of change points under standard regularity assumptions. We compare the proposed approach with competing methods in a simulation study. Methods from cluster analysis are applied to assess performance and to allow simple comparisons of location estimates, even when the estimated number differs. We conclude with applications in genetics, finance, and spatio-temporal analysis. Supplementary materials for this article are available online.

Subfields: Genetics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8bff658feca67f50993069b1782f6dc222ec6af3

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Citations in the corpus

Heterogeneous change point inference (2015, methodology): “s therein. In addition, methods which search for more general structural changes in the distribution potentially apply to this setup as well, see e.g. (Csorgo and Horvath, 1997; Arlot et al., 2012; Matteson and James, 2014). This is in contrast to the setting we address in this paper: Motivated by t”
Change-point detection in high-dimensional covariance structure (2016, methodology): “As an alternative, permutation [28] [31] or parametric bootstrap may be used [28].”
ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data (2013, methodology): “The goodness-of-fit statistic used in Matteson and James (2013) is the between-within distance (Székely and Rizzo, 2005) among adjacent segments.”
Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data (2017, methodology): “Nonparametric methods have been proposed for the change-point detection problem for multivariate/non-Euclidean observations as well (Jirak et al. (2015), Matteson and James (2014), Lung-Yut-Fong, L´evy-Leduc and Capp´e (2011), Cule, Samworth and Stewart (2010), Desobry, Davy and Don-carli (2005)).”
Wild binary segmentation for multiple change-point detection (2014, background): “We note that Matteson and James (2014) provide theoretical consistency results for a method related to the latter, but not windowed and hence computationally intensive, in the case of a bounded number of change-points.”
M-Statistic for Kernel Change-Point Detection (2015, methodology): “ the estimation error. In the ofﬂine setting, Zou et al. (2014b) study a problem when there are sanomalous sequences out of nsequences to be detected, and the test statistic is constructed using MMD; Matteson and James (2014) propose a nonparametric approach based on 3 U-statistics and adopt the hie”