Minimax and bayes estimation in deconvolution problem*
Mechanical Engineering Problems Institute,
Mechanical Engineering Problems Institute, Russian Academy of Sciences,
Bolshoy pr. VO 61, 199178 St.Petersburg, Russia.
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 Series 36 (2001) 419–433].
Mathematics Subject Classification: 62G05 / 65R30 / 65R32
Key words: Deconvolution / minimax estimation / Bayes estimation / Wiener filtration
© EDP Sciences, SMAI, 2008