Multiple testing of local extrema for detection of change points

Dan Cheng, Zhibing He, Armin Schwartzman

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3705-3729
Number of pages25
JournalElectronic Journal of Statistics
Volume14
Issue number2
DOIs
StatePublished - 2020

Keywords

  • Change points
  • Differential
  • FDR
  • Gaussian processes
  • Kernel smoothing
  • Local maxima
  • Local minima
  • Multiple testing
  • Power

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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