Minimax and bayes estimation in deconvolution problem*

Mikhail Ermakov

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 327-344
  • ISSN: 1292-8100

Abstract

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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 and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii, IMS Lecture Notes Monograph Series36 (2001) 419–433].

How to cite

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Ermakov, Mikhail. "Minimax and bayes estimation in deconvolution problem*." ESAIM: Probability and Statistics 12 (2008): 327-344. <http://eudml.org/doc/250407>.

@article{Ermakov2008,
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 and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii, IMS Lecture Notes Monograph Series36 (2001) 419–433]. },
author = {Ermakov, Mikhail},
journal = {ESAIM: Probability and Statistics},
keywords = {Deconvolution; minimax estimation; Bayes estimation; Wiener filtration; deconvolution},
language = {eng},
month = {5},
pages = {327-344},
publisher = {EDP Sciences},
title = {Minimax and bayes estimation in deconvolution problem*},
url = {http://eudml.org/doc/250407},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Ermakov, Mikhail
TI - Minimax and bayes estimation in deconvolution problem*
JO - ESAIM: Probability and Statistics
DA - 2008/5//
PB - EDP Sciences
VL - 12
SP - 327
EP - 344
AB - 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 and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii, IMS Lecture Notes Monograph Series36 (2001) 419–433].
LA - eng
KW - Deconvolution; minimax estimation; Bayes estimation; Wiener filtration; deconvolution
UR - http://eudml.org/doc/250407
ER -

References

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

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