We study problem of the minimax estimation of a nonparametric signal blurred by some known function and observed with additive noise. The unknown function is assumed to belong to an ellipsoid in L_2([0,1]). We propose a linear estimator and show that its maximal risk, under some conditions, has the same asymptotic behavior as the minimax risk. We also derive the exact asymptotics of the minimal risk. The results are illustrated by one example.
|Title of host publication||Probability Theory and Mathematical Statistics (Proceeedings of the Seventh Vilnius Conference, Vilnius, Lithuania, August 12-18, 1998)|
|Editors||B. Grigelionis, J. Kubilius, V. Paulauskas, H. Pragarauskas, R. Rudzkis, V. Statulevicius|
|Place of Publication||Vilnius|
|Publication status||Published - 1999|