The Annals of Statistics

Estimating deformations of stationary processes

Maureen Clerc and Stéphane Mallat

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Abstract

This paper studies classes of nonstationary processes, such as warped processes and frequency-modulated processes, that result from the deformation of stationary processes. Estimating deformations can often provide important information about an underlying physical phenomenon. A computational harmonic analysis viewpoint shows that the deformed autocovariance satisfies a transport equation at small scales, with a velocity proportional to a deformation gradient. We derive an estimator of the deformation from a single realization of the deformed process, with a proof of consistency under appropriate assumptions.

Article information

Source
Ann. Statist., Volume 31, Number 6 (2003), 1772-1821.

Dates
First available in Project Euclid: 16 January 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1074290327

Digital Object Identifier
doi:10.1214/aos/1074290327

Mathematical Reviews number (MathSciNet)
MR2036390

Zentralblatt MATH identifier
1052.62086

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G12: General second-order processes
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

Keywords
Nonstationary processes inverse problem wavelets warping frequency modulation scalogram spectrogram

Citation

Clerc, Maureen; Mallat, Stéphane. Estimating deformations of stationary processes. Ann. Statist. 31 (2003), no. 6, 1772--1821. doi:10.1214/aos/1074290327. https://projecteuclid.org/euclid.aos/1074290327


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