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2020 Multiple testing of local extrema for detection of change points
Dan Cheng, Zhibing He, Armin Schwartzman
Electron. J. Statist. 14(2): 3705-3729 (2020). DOI: 10.1214/20-EJS1751

Abstract

A new approach to detect change points based on differential smoothing and multiple testing is presented for long data sequences modeled as piecewise constant functions plus stationary ergodic Gaussian noise. As an application of the STEM algorithm for peak detection developed in Schwartzman et al. [27] and Cheng and Schwartzman [5], the method detects change points as significant local maxima and minima after smoothing and differentiating the observed sequence. The algorithm, combined with the Benjamini-Hochberg procedure for thresholding p-values, provides asymptotic strong control of the False Discovery Rate (FDR) and power consistency, as the length of the sequence and the size of the jumps get large. Simulations show that FDR levels are maintained in non-asymptotic conditions and guide the choice of smoothing bandwidth. The methods are illustrated in magnetometer sensor data and genomic array-CGH data. An R package named “dSTEM” is available in R Cran.

Citation

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Dan Cheng. Zhibing He. Armin Schwartzman. "Multiple testing of local extrema for detection of change points." Electron. J. Statist. 14 (2) 3705 - 3729, 2020. https://doi.org/10.1214/20-EJS1751

Information

Received: 1 November 2019; Published: 2020
First available in Project Euclid: 7 October 2020

zbMATH: 07270275
MathSciNet: MR4159178
Digital Object Identifier: 10.1214/20-EJS1751

Subjects:
Primary: 62M07, 62M10
Secondary: 60G15, 60G35

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Vol.14 • No. 2 • 2020
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