ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM—TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS

Matt Sourisseau; Hau Tieng Wu; Zhou Zhou

doi:10.1214/22-AOS2203

ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM—TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS

Matt Sourisseau, Hau Tieng Wu, Zhou Zhou

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	2694-2712
Number of pages	19
Journal	Annals of Statistics
Volume	50
Issue number	5
DOIs	https://doi.org/10.1214/22-AOS2203
State	Published - Oct 2022

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/22-AOS2203

Cite this

@article{6d2bd262f4cf4c259f47cf2c5c7d70a1,

title = "ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM—TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS",

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.",

keywords = "CR calculation, Synchrosqueezing transform, complex Gaussian random vector, kernel regression, time series analysis",

author = "Matt Sourisseau and Wu, {Hau Tieng} and Zhou Zhou",

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022.",

year = "2022",

month = oct,

doi = "10.1214/22-AOS2203",

language = "English (US)",

volume = "50",

pages = "2694--2712",

journal = "Annals of Statistics",

issn = "0090-5364",

publisher = "Institute of Mathematical Statistics",

number = "5",

}

TY - JOUR

T1 - ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM—TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS

AU - Sourisseau, Matt

AU - Wu, Hau Tieng

AU - Zhou, Zhou

N1 - Funding Information: 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. Publisher Copyright: © Institute of Mathematical Statistics, 2022.

PY - 2022/10

Y1 - 2022/10

N2 - 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.

AB - 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.

KW - CR calculation

KW - Synchrosqueezing transform

KW - complex Gaussian random vector

KW - kernel regression

KW - time series analysis

UR - http://www.scopus.com/inward/record.url?scp=85146131686&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85146131686&partnerID=8YFLogxK

U2 - 10.1214/22-AOS2203

DO - 10.1214/22-AOS2203

M3 - Article

AN - SCOPUS:85146131686

SN - 0090-5364

VL - 50

SP - 2694

EP - 2712

JO - Annals of Statistics

JF - Annals of Statistics

IS - 5

ER -

ASYMPTOTIC ANALYSIS OF SYNCHROSQUEEZING TRANSFORM—TOWARD STATISTICAL INFERENCE WITH NONLINEAR-TYPE TIME-FREQUENCY ANALYSIS

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this