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Spectra in low‐rank localized layers (SpeLLL) for interpretable time–frequency analysis

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  • Marie Tuft
  • Martica H. Hall
  • Robert T. Krafty

Abstract

The time‐varying frequency characteristics of many biomedical time series contain important scientific information. However, the high‐dimensional nature of the time‐varying power spectrum as a surface in time and frequency limits its direct use by applied researchers and clinicians for elucidating complex mechanisms. In this article, we introduce a new approach to time–frequency analysis that decomposes the time‐varying power spectrum in to orthogonal rank‐one layers in time and frequency to provide a parsimonious representation that illustrates relationships between power at different times and frequencies. The approach can be used in fully nonparametric analyses or in semiparametric analyses that account for exogenous information and time‐varying covariates. An estimation procedure is formulated within a penalized reduced‐rank regression framework that provides estimates of layers that are interpretable as power localized within time blocks and frequency bands. Empirical properties of the procedure are illustrated in simulation studies and its practical use is demonstrated through an analysis of heart rate variability during sleep.

Suggested Citation

  • Marie Tuft & Martica H. Hall & Robert T. Krafty, 2023. "Spectra in low‐rank localized layers (SpeLLL) for interpretable time–frequency analysis," Biometrics, The International Biometric Society, vol. 79(1), pages 304-318, March.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:1:p:304-318
    DOI: 10.1111/biom.13577
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    References listed on IDEAS

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    1. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Robert T. Krafty, 2016. "Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 435-450, July.
    4. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    5. Scott A. Bruce & Cheng Yong Tang & Martica H. Hall & Robert T. Krafty, 2020. "Empirical Frequency Band Analysis of Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1933-1945, December.
    6. Kun Chen & Kung‐Sik Chan & Nils Chr. Stenseth, 2012. "Reduced rank stochastic regression with a sparse singular value decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 203-221, March.
    7. Claudia Kirch & Birte Muhsal & Hernando Ombao, 2015. "Detection of Changes in Multivariate Time Series With Application to EEG Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1197-1216, September.
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