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

Presented by: 
Yining Chen
Thursday 31st May 2018 - 11:00 to 12:00
INI Seminar Room 2
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). NOT offers highly competitive performance when being applied together with some information criteria. For selected scenarios, we show the consistency and near-optimality of NOT in detecting the number and locations of generalised change-points. The computational complexity as well as its extensions will also be discussed.

(Joint work with Rafal Baranowski and Piotr Fryzlewicz.)

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons