Abstract
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.
Acknowledgments
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.
Citation
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
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