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Article overview
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Narrowest-Over-Threshold Detection of Multiple Change-points and Change-point-like Features | Rafal Baranowski
; Yining Chen
; Piotr Fryzlewicz
; | Date: |
1 Sep 2016 | Abstract: | We propose a new, generic and flexible methodology for nonparametric 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 generalised
change-points.
Our methodology works with only minor modifications across a range of
generalised change-point scenarios, and we achieve such a high degree of
generality by proposing and using a new multiple generalised change-point
detection device, termed Narrowest-Over-Threshold (NOT). The key ingredient of
NOT is its focus on the smallest local sections of the data on which the
existence of a feature is suspected. Crucially, this adaptive localisation
technique prevents NOT from considering subsamples containing two or more
features, a key factor that ensures the general applicability of NOT.
For selected scenarios, we show the consistency and near-optimality of NOT in
detecting the number and locations of generalised change-points, and discuss
how to extend the proof to other settings. The NOT estimators are easy to
implement and rapid to compute: the entire threshold-indexed solution path can
be computed in close-to-linear time. Importantly, the NOT approach is easy to
extend by the user to tailor to their own needs. There is no single competitor,
but we show that the performance of NOT matches or surpasses the state of the
art in the scenarios tested. Our methodology is implemented in the R package
extbf{not}. | Source: | arXiv, 1609.0293 | Services: | Forum | Review | PDF | Favorites |
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