Open Access
December 2011 Multiple testing of local maxima for detection of peaks in 1D
Armin Schwartzman, Yulia Gavrilov, Robert J. Adler
Ann. Statist. 39(6): 3290-3319 (December 2011). DOI: 10.1214/11-AOS943


A topological multiple testing scheme for one-dimensional domains is proposed where, rather than testing every spatial or temporal location for the presence of a signal, tests are performed only at the local maxima of the smoothed observed sequence. Assuming unimodal true peaks with finite support and Gaussian stationary ergodic noise, it is shown that the algorithm with Bonferroni or Benjamini–Hochberg correction provides asymptotic strong control of the family wise error rate and false discovery rate, and is power consistent, as the search space and the signal strength get large, where the search space may grow exponentially faster than the signal strength. Simulations show that error levels are maintained for nonasymptotic conditions, and that power is maximized when the smoothing kernel is close in shape and bandwidth to the signal peaks, akin to the matched filter theorem in signal processing. The methods are illustrated in an analysis of electrical recordings of neuronal cell activity.


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Armin Schwartzman. Yulia Gavrilov. Robert J. Adler. "Multiple testing of local maxima for detection of peaks in 1D." Ann. Statist. 39 (6) 3290 - 3319, December 2011.


Published: December 2011
First available in Project Euclid: 5 March 2012

zbMATH: 1246.62173
MathSciNet: MR3012409
Digital Object Identifier: 10.1214/11-AOS943

Primary: 62H15
Secondary: 62M10

Keywords: False discovery rate , Gaussian process , kernel smoothing , matched filter , topological inference

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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