ON OPTIMAL-SOLUTIONS OF THE DECONVOLUTION PROBLEM

The asymptotic behaviour of minimax and Bayes risks are studied for the deconvolution problem as a power of noise tends to zero. Under wide assumptions the author shows that the convergence order of the regularization method does not depend on the regularizer and is optimal for both Bayes and minimax risks. The author finds the connection between the orders of convergence of minimax and Bayes risks and proposes a simple algorithm for their calculation.