Title: On minimax nonparametric estimation of signal in Gaussian noise,
Abstract: For the problem of nonparametric estimation of signal in Gaussian noise we
point out the strong asymptotically minimax estimators on maxisets for linear
estimators (see \cite{ker93,rio}). It turns out that the order of rates of
convergence of Pinsker estimator on this maxisets is worse than the order of
rates of convergence for the class of linear estimators considered on this
maxisets. We show that balls in Sobolev spaces are maxisets for Pinsker
estimators.