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SURE shrinkage of Gaussian paths and signal identification*

Published online by Cambridge University Press:  05 January 2012

Nicolas Privault  and
Anthony Réveillac
Nicolas Privault
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore. [email protected]
Anthony Réveillac
Affiliation:
Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France. [email protected]
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Abstract

Using integration by parts on Gaussian spacewe construct a Stein Unbiased Risk Estimator (SURE)for the drift of Gaussian processes, based on theirlocal and occupation times.By almost-sure minimization of the SURE risk ofshrinkage estimators we derive an estimation and de-noisingprocedure for an input signal perturbed by acontinuous-time Gaussian noise.

Keywords

EstimationSURE shrinkagethresholdingdenoisingGaussian processesMalliavin calculus
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 15: Supplement: In honor of Marc Yor , 2011 , pp. 180 - 196
Copyright
© EDP Sciences, SMAI, 2011

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