We study nonparametric estimation of a signal in Gaussian white noise on maxisets. We point out minimax estimators in the class of all linear estimators and strong asymptotically minimax estimators in the class of all estimators. We show that balls in Sobolev spaces are maxisets for the Pinsker estimators.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 120–133.
Translated by M. Ermakov.
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Ermakov, M. Minimax Nonparametric Estimation on Maxisets. J Math Sci 244, 779–788 (2020). https://doi.org/10.1007/s10958-020-04651-1
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DOI: https://doi.org/10.1007/s10958-020-04651-1