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December 2003 Estimating deformations of stationary processes
Maureen Clerc, Stéphane Mallat
Ann. Statist. 31(6): 1772-1821 (December 2003). DOI: 10.1214/aos/1074290327


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.


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Maureen Clerc. Stéphane Mallat. "Estimating deformations of stationary processes." Ann. Statist. 31 (6) 1772 - 1821, December 2003.


Published: December 2003
First available in Project Euclid: 16 January 2004

zbMATH: 1052.62086
MathSciNet: MR2036390
Digital Object Identifier: 10.1214/aos/1074290327

Primary: 60G12 , 62M10
Secondary: 60G35

Keywords: frequency modulation , inverse problem , nonstationary processes , scalogram , spectrogram , warping , Wavelets

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 6 • December 2003
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