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.
Mots clés : estimation, sure shrinkage, thresholding, denoising, gaussian processes, Malliavin calculus
@article{PS_2011__15__180_0, author = {Privault, Nicolas and R\'eveillac, Anthony}, title = {SURE shrinkage of gaussian paths and signal identification}, journal = {ESAIM: Probability and Statistics}, pages = {180--196}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2009013}, mrnumber = {2870511}, zbl = {1261.93078}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2009013/} }
TY - JOUR AU - Privault, Nicolas AU - Réveillac, Anthony TI - SURE shrinkage of gaussian paths and signal identification JO - ESAIM: Probability and Statistics PY - 2011 SP - 180 EP - 196 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2009013/ DO - 10.1051/ps/2009013 LA - en ID - PS_2011__15__180_0 ER -
%0 Journal Article %A Privault, Nicolas %A Réveillac, Anthony %T SURE shrinkage of gaussian paths and signal identification %J ESAIM: Probability and Statistics %D 2011 %P 180-196 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2009013/ %R 10.1051/ps/2009013 %G en %F PS_2011__15__180_0
Privault, Nicolas; Réveillac, Anthony. SURE shrinkage of gaussian paths and signal identification. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 180-196. doi : 10.1051/ps/2009013. http://www.numdam.org/articles/10.1051/ps/2009013/
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