Minimax and Bayes estimation in deconvolution problem
- Ermakov, Mikhail S.
2010 Mathematics Subject Classification
- deconvolution, minimax estimation, Bayes estimation, Wiener filtration
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 .