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Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 120–133 (Mi znsl6545)  

This article is cited in 1 scientific paper (total in 1 paper)

On minimax nonparametric estimation on maxisets

M. S. Ermakovab

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia

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. 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.

Key words and phrases: Tikhonov regularization algorithm, maximum likelihood estimator, asymptotically minimax estimation, nonparametric estimation.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00828


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Document Type: Article
UDC: 519.2
Received: 14.11.2017

Citation: M. S. Ermakov, “On minimax nonparametric estimation on maxisets”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 120–133

Citation in format AMSBIB
\Bibitem{Erm17}
\by M.~S.~Ermakov
\paper On minimax nonparametric estimation on maxisets
\inbook Probability and statistics. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 466
\pages 120--133
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6545}


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  • http://mi.mathnet.ru/eng/znsl/v466/p120

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. S. Ermakov, “Ob asimptoticheski minimaksnom obnaruzhenii signala v gaussovskom belom shume”, Veroyatnost i statistika. 27, Zap. nauchn. sem. POMI, 474, POMI, SPb., 2018, 124–138  mathnet
  • Записки научных семинаров ПОМИ
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