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Article Dans Une Revue Annals of Statistics Année : 2003

Estimating deformations of stationary processes

Résumé

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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Dates et versions

hal-00150387 , version 1 (30-05-2007)

Identifiants

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Maureen Clerc, Stéphane Mallat. Estimating deformations of stationary processes. Annals of Statistics, 2003, 31 (6), pp. 1772-1821. ⟨10.1214/aos/1074290327⟩. ⟨hal-00150387⟩
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