Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation

References

• Adak, S. (1998), “Time-Dependent Spectral Analysis of Nonstationary Time Series,” Journal of the American Statistical Association, 93, 1488–1501. DOI: 10.1080/01621459.1998.10473808.
   Web of Science ®Google Scholar
• Benchetrit, G. (2000), “Breathing Pattern in Humans: Diversity and Individuality,” Respiration Physiology, 122, 123–129. DOI: 10.1016/s0034-5687(00)00154-7.
   PubMedGoogle Scholar
• Bruna, J., Mallat, S., Bacry, E., Muzy, J., et al. (2015), “Intermittent Process Analysis with Scattering Moments,” Annals of Statistics, 43, 323–351.
   Web of Science ®Google Scholar
• Chen, Y.-C., Cheng, M.-Y., and Wu, H.-T. (2014). Nonparametric and adaptive modeling of dynamic seasonality and trend with heteroscedastic and dependent errors. Journal of the Royal Statistical Society, Series B, 76, 651–682. DOI: 10.1111/rssb.12039.
   Google Scholar
• Chernozhukov, V., Chetverikov, D., and Kato, K. (2013), “Gaussian Approximations and Multiplier Bootstrap for Maxima of Sums of High-Dimensional Random Vectors,” The Annals of Statistics, 41, 2786–2819. DOI: 10.1214/13-AOS1161.
   Web of Science ®Google Scholar
• Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia: SIAM.
   Google Scholar
• Davis, R. A., and Mikosch, T. (1999), “The Maximum of the Periodogram of a Non-Gaussian Sequence,” Annals of Probability, 27, 522–536.
   Web of Science ®Google Scholar
• De Gennaro, L., Ferrara, M. (2003), “Sleep Spindles: An Overview,” Sleep Medicine Reviews, 7, 423–440. DOI: 10.1053/smrv.2002.0252.
   PubMed Web of Science ®Google Scholar
• Dette, H., and Gösmann, J. (2018), “Relevant Change Points in High Dimensional Time Series,” Electronic Journal of Statistics, 12, 2578–2636. DOI: 10.1214/18-EJS1464.
   Web of Science ®Google Scholar
• Dwivedi, Y., and Subba Rao, S. (2011), “A Test for Second-Order Stationarity of a Time Series based on the Discrete Fourier Transform,” Journal of Time Series Analysis, 32, 68–91. DOI: 10.1111/j.1467-9892.2010.00685.x.
   Web of Science ®Google Scholar
• Flandrin, P. (1998), Time-Frequency/Time-Scale Analysis, San Diego: Academic Press.
   Google Scholar
• Genton, M. G., Hall, P. (2007), “Statistical Inference for Evolving Periodic Functions,” Journal of the Royal Statistical Society, Series B, 69, 643–657. DOI: 10.1111/j.1467-9868.2007.00604.x.
   Google Scholar
• Iber, C., Ancoli-Isreal, S., Chesson Jr., A. L., and Quan, S. F. (2007), The AASM Manual for Scoring of Sleep and Associated Events-Rules: Terminology and Technical Specification, Darien, IL: AASM.
   Google Scholar
• Jirak, M. (2015), “Uniform Change Point Tests in High Dimension,” Annals of Statistics, 43, 2451–2483.
   Web of Science ®Google Scholar
• Last, M., and Shumway, R. (2008), “Detecting Abrupt Changes in a Piecewise Locally Stationary Time Series,” Journal of Multivariate Analysis, 99, 191–214. DOI: 10.1016/j.jmva.2007.06.010.
   PubMed Web of Science ®Google Scholar
• Lavielle, M., Ludeña, C. (2000), “The Multiple Change-Points Problem for the Spectral Distribution,” Bernoulli, 6, 845–869. DOI: 10.2307/3318759.
   Web of Science ®Google Scholar
• Lin, Z., Liu, W. (2009), “On Maxima of Periodograms of Stationary Processes,” The Annals of Statistics, 37, 2676–2695. DOI: 10.1214/08-AOS590.
   Web of Science ®Google Scholar
• Liu, G.-R., Sheu, Y.-C., and Wu, H.-T. (2022), “Asymptotic Analysis of Higher-Order Scattering Transform of Gaussian Processes,” Electronic Journal of Probability, 27, 1–27. DOI: 10.1214/22-EJP766.
   Web of Science ®Google Scholar
• Malik, M. (1996), “Heart Rate Variability: Standards of Measurement, Physiological Interpretation, and Clinical Use: Task Force of the European Society of Cardiology and the North American Society for Pacing and Electrophysiology,” Annals of Noninvasive Electrocardiology, 1, 151–181. DOI: 10.1111/j.1542-474X.1996.tb00275.x.
   Google Scholar
• Nason, G. P., Von Sachs, R., and Kroisandt, G. (2000), “Wavelet Processes and Adaptive Estimation of the Evolutionary Wavelet Spectrum,” Journal of the Royal Statistical Society, Series B, 62, 271–292. DOI: 10.1111/1467-9868.00231.
   Google Scholar
• Nazarov, F. (2003). Geometric Aspects of Functional Analysis: Israel Seminar 2001-2002, Berlin: Springer.
   Google Scholar
• Preuss, P., Puchstein, R., Dette, H. (2015), “Detection of Multiple Structural Breaks in Multivariate Time Series,” Journal of the American Statistical Association, 110, 654–668. DOI: 10.1080/01621459.2014.920613.
   Web of Science ®Google Scholar
• Sourisseau, M., Wu, H.-T., and Zhou, Z. (2022), “Inference of Synchrosqueezing Transform–Toward a Unified Statistical Analysis of Nonlinear-Type Time-Frequency Analysis,” Annals of Statistics.
   Web of Science ®Google Scholar
• Stein, C. (1986), “Approximate Computation of Expectations,” Lecture Notes-Monograph Series, 7, i–164.
   Google Scholar
• Zhang, D., Wu, W. B. (2017), “Gaussian Approximation for High Dimensional Time Series,” Annals of Statistics, 45, 1895–1919.
   Web of Science ®Google Scholar
• Zhang, X., Cheng, G. (2018), “Gaussian Approximation for High Dimensional Vector Under Physical Dependence,” Bernoulli, 24, 2640–2675. DOI: 10.3150/17-BEJ939.
   Web of Science ®Google Scholar
• Zhou, Z. (2013), “Heteroscedasticity and Autocorrelation Robust Structural Change Detection,” Journal of the American Statistical Association, 108, 726–740. DOI: 10.1080/01621459.2013.787184.
   Web of Science ®Google Scholar
• Zhou, Z. (2014), “Inference of Weighted v-statistics for Nonstationary Time Series and its Applications,” Annals of Statistics, 42, 87–114.
   Web of Science ®Google Scholar