Electronic Journal of Statistics

FDR-control in multiscale change-point segmentation

Housen Li, Axel Munk, and Hannes Sieling

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 918-959.

Dates
Received: October 2015
First available in Project Euclid: 8 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1460141648

Digital Object Identifier
doi:10.1214/16-EJS1131

Mathematical Reviews number (MathSciNet)
MR3486421

Zentralblatt MATH identifier
1338.62117

Subjects
Primary: 62G08: Nonparametric regression 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 90C39: Dynamic programming [See also 49L20]

Keywords
Multiscale inference change-point regression false discovery rate deviation bound dynamic programming minimax lower bound honest inference array CGH data ion channel recordings

Citation

Li, Housen; Munk, Axel; Sieling, Hannes. FDR-control in multiscale change-point segmentation. Electron. J. Statist. 10 (2016), no. 1, 918--959. doi:10.1214/16-EJS1131. https://projecteuclid.org/euclid.ejs/1460141648


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