Minimax recovery of blurred signal from discrete noisy data

Abstract

The problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise is considered. The unknown function is assumed to belong to a hyperrectangle in L ₂-([0,l]). Under some conditions, we find the exact asymptotic behavior of the quadratic minimax risk. We propose an estimator and show that its maximal risk attains asymptotically the minimax risk. The results are illustrated by examples.

Keywords:

• Blurred signal
• Exact asymptotics of the minimax risk
• Hyperrectangle