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2016 FDR-control in multiscale change-point segmentation
Housen Li, Axel Munk, Hannes Sieling
Electron. J. Statist. 10(1): 918-959 (2016). DOI: 10.1214/16-EJS1131

Abstract

Fast multiple change-point segmentation methods, which additionally provide faithful statistical statements on the number, locations and sizes of the segments, have recently received great attention. In this paper, we propose a multiscale segmentation method, FDRSeg, which controls the false discovery rate (FDR) in the sense that the number of false jumps is bounded linearly by the number of true jumps. In this way, it adapts the detection power to the number of true jumps. We prove a non-asymptotic upper bound for its FDR in a Gaussian setting, which allows to calibrate the only parameter of FDRSeg properly. Moreover, we show that FDRSeg estimates change-point locations, as well as the signal, in a uniform sense at optimal minimax convergence rates up to a log-factor. The latter is w.r.t. $L^{p}$-risk, $p\ge 1$, over classes of step functions with bounded jump sizes and either bounded, or even increasing, number of change-points. FDRSeg can be efficiently computed by an accelerated dynamic program; its computational complexity is shown to be linear in the number of observations when there are many change-points. The performance of the proposed method is examined by comparisons with some state of the art methods on both simulated and real datasets. An R-package is available online.

Citation

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Housen Li. Axel Munk. Hannes Sieling. "FDR-control in multiscale change-point segmentation." Electron. J. Statist. 10 (1) 918 - 959, 2016. https://doi.org/10.1214/16-EJS1131

Information

Received: 1 October 2015; Published: 2016
First available in Project Euclid: 8 April 2016

zbMATH: 1338.62117
MathSciNet: MR3486421
Digital Object Identifier: 10.1214/16-EJS1131

Subjects:
Primary: 62G08, 62G10, 62G20
Secondary: 90C39

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.10 • No. 1 • 2016
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