On minimax nonparametric estimation of signal in Gaussian noise

الأصل · EN

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 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.