October 2022 Asymptotic analysis of synchrosqueezing transform—toward statistical inference with nonlinear-type time-frequency analysis
Matt Sourisseau, Hau-Tieng Wu, Zhou Zhou
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Ann. Statist. 50(5): 2694-2712 (October 2022). DOI: 10.1214/22-AOS2203


We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and nonnull cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then a central limit theorem result for SST is established. As an example, we provide a block bootstrap scheme based on the established SST theory to test if a given time series contains oscillatory components.


The authors acknowledge Professors Almut Burchard and Mary Pugh for the fruitful discussion. They thank the authors of [8] for providing the ChirpLab 1.1 code. They also thank the Associate Editor and the anonymous reviewers for their valuable and constructive feedbacks and comments.


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Matt Sourisseau. Hau-Tieng Wu. Zhou Zhou. "Asymptotic analysis of synchrosqueezing transform—toward statistical inference with nonlinear-type time-frequency analysis." Ann. Statist. 50 (5) 2694 - 2712, October 2022. https://doi.org/10.1214/22-AOS2203


Received: 1 May 2021; Revised: 1 March 2022; Published: October 2022
First available in Project Euclid: 27 October 2022

MathSciNet: MR4505374
zbMATH: 07628837
Digital Object Identifier: 10.1214/22-AOS2203

Primary: 60K35

Keywords: complex Gaussian random vector , CR calculation , kernel regression , Synchrosqueezing transform , time series analysis

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 5 • October 2022
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