Narrowest-over-threshold detection of multiple change points and change-point-like features

Baranowski, Rafal, Chen, Yining ORCID: 0000-0003-1697-1920 and Fryzlewicz, Piotr ORCID: 0000-0002-9676-902X (2019) Narrowest-over-threshold detection of multiple change points and change-point-like features. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 81 (3). 649 - 672. ISSN 1369-7412

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Abstract

We propose a new, generic and flexible methodology for non-parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar irregularities, which we also refer to as generalized change points. Our methodology works with only minor modifications across a range of generalized change point scenarios, and we achieve such a high degree of generality by proposing and using a new multiple generalized change point detection device, termed narrowest-over-threshold (NOT) detection. The key ingredient of the NOT method is its focus on the smallest local sections of the data on which the existence of a feature is suspected. For selected scenarios, we show the consistency and near optimality of the NOT algorithm in detecting the number and locations of generalized change points. The NOT estimators are easy to implement and rapid to compute. Importantly, the NOT approach is easy to extend by the user to tailor to their own needs. Our methodology is implemented in the R package not.

Item Type:	Article
Additional Information:	© 2019 Royal Statistical Society
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	09 Apr 2019 10:42
Last Modified:	14 Nov 2024 21:33
URI:	http://eprints.lse.ac.uk/id/eprint/100430

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