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Minimax and bayes estimationin deconvolution problem*

Published online by Cambridge University Press:  08 May 2008

Mikhail Ermakov
Mikhail Ermakov*
Affiliation:
Mechanical Engineering Problems Institute, Mechanical Engineering Problems Institute, Russian Academy of Sciences, Bolshoy pr. VO 61, 199178 St.Petersburg, Russia.
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Abstract

We consider a deconvolution problem of estimating a signal blurred with a random noise.The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax andBayes estimators. In the case of solutions having finite number ofderivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii, IMS Lecture Notes Monograph Series36 (2001) 419–433].

Keywords

Deconvolutionminimax estimationBayes estimationWiener filtration
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 327 - 344
Copyright
© EDP Sciences, SMAI, 2008

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* This paper was partially supported by RFFI Grants 02-01-00262, 4422.2006.1.