WIAS Preprint No. 982, (2004)

Minimax and Bayes estimation in deconvolution problem



Authors

  • Ermakov, Mikhail S.

2010 Mathematics Subject Classification

  • 62G05

Keywords

  • deconvolution, minimax estimation, Bayes estimation, Wiener filtration

Abstract

We consider the problem of estimation of solution of convolution equation on observations blurred a random noise. The noise is a product of Gaussian stationary process and a weight function $epsilon h in L_2(R1)$ with constant $epsilon > 0$. The presence of weight function $h$ makes the power of noise finite on $R1$. This allows to suppose that the power of solution is also finite. For this model we find asymptotically minimax and Bayes estimators. The solution is supposed infinitely differentiable. The model with solutions having finite number of derivatives was studied in [5].

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