Minimax and Bayes estimation in deconvolution problem

Ermakov, Mikhail

ESAIM: Probability and Statistics, Tome 12 (2008), pp. 327-344.

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 $h\in L_2\left(R^1\right)$ 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 Series 36 (2001) 419-433].

Classification : 62G05, 65R30, 65R32
Mots clés : deconvolution, minimax estimation, Bayes estimation, Wiener filtration

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