SURE shrinkage of Gaussian paths and signal identification*

Nicolas Privault; Anthony Réveillac

ESAIM: Probability and Statistics (2012)

  • Volume: 15, page 180-196
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Privault, Nicolas, and Réveillac, Anthony. "SURE shrinkage of Gaussian paths and signal identification*." ESAIM: Probability and Statistics 15 (2012): 180-196. <http://eudml.org/doc/222468>.

@article{Privault2012,
abstract = { 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. },
author = {Privault, Nicolas, Réveillac, Anthony},
journal = {ESAIM: Probability and Statistics},
keywords = {Estimation; SURE shrinkage; thresholding; denoising; Gaussian processes; Malliavin calculus; estimation; Gaussian processes; shrinkage of Gaussian paths; continuous-time Gaussian noise; Stein unbiased risk; input signal; occupation times; signal identification},
language = {eng},
month = {1},
pages = {180-196},
publisher = {EDP Sciences},
title = {SURE shrinkage of Gaussian paths and signal identification*},
url = {http://eudml.org/doc/222468},
volume = {15},
year = {2012},
}

TY - JOUR
AU - Privault, Nicolas
AU - Réveillac, Anthony
TI - SURE shrinkage of Gaussian paths and signal identification*
JO - ESAIM: Probability and Statistics
DA - 2012/1//
PB - EDP Sciences
VL - 15
SP - 180
EP - 196
AB - 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.
LA - eng
KW - Estimation; SURE shrinkage; thresholding; denoising; Gaussian processes; Malliavin calculus; estimation; Gaussian processes; shrinkage of Gaussian paths; continuous-time Gaussian noise; Stein unbiased risk; input signal; occupation times; signal identification
UR - http://eudml.org/doc/222468
ER -

References

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  16. N. Privault and A. Réveillac, Stein estimation of Poisson process intensities. Stat. Inference Stoch. Process.12 (2009) 37–53.  Zbl1205.62123
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