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 Zap. Nauchn. Sem. POMI, 2017, Volume 466, Pages 289–299 (Mi znsl6555)

A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise

V. N. Solevab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia

Abstract: In the paper, we construct the lower and upper bounds of the minimax risk in the estimation problem, as we observe the unknoun pseudo periodic function in stationary noise with a density satisfying the local version of the Muckenhoupt condition.

Key words and phrases: pseudo periodic function, nonparametric estimating, process with stationary increments.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-01-00828 Russian Academy of Sciences - Federal Agency for Scientific Organizations PRAS-18-01

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Document Type: Article
UDC: 519.2

Citation: V. N. Solev, “A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise”, Probability and statistics. Part 26, Zap. Nauchn. Sem. POMI, 466, POMI, St. Petersburg, 2017, 289–299

Citation in format AMSBIB
\Bibitem{Sol17} \by V.~N.~Solev \paper A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise \inbook Probability and statistics. Part~26 \serial Zap. Nauchn. Sem. POMI \yr 2017 \vol 466 \pages 289--299 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6555}