Volume 15, 2011
|Page(s)||180 - 196|
|Published online||05 January 2012|
SURE shrinkage of Gaussian paths and signal identification*
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore. firstname.lastname@example.org
2 Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France. email@example.com
Revised: 24 July 2009
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes, based on their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.
Mathematics Subject Classification: 93E10 / 93E14 / 60G35 / 60H07
Key words: Estimation / SURE shrinkage / thresholding / denoising / Gaussian processes / Malliavin calculus
© EDP Sciences, SMAI, 2011
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