| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 180 - 196 | |
| DOI | https://doi.org/10.1051/ps/2009013 | |
| Published online | 05 January 2012 | |
SURE shrinkage of Gaussian paths and signal identification*
1
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore. nprivault@ntu.edu.sg
2
Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16,
France. anthony.reveillac@ceremade.dauphine.fr
Received:
24
February
2009
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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