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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2016 Volume 454, Pages 261–275 (Mi znsl6398)

This article is cited in 7 papers

Adaptive estimation of function observed in Gaussian 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 article we propose an adaptive estimation of the unknown pseudo periodic function which observed in stationary noise with the unknown spectral density which belongs to a given class. We compare the accuracy of the proposed estimation with the minimax risk and give a lower bound for the minimax risk.

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

UDC: 519.2

Received: 20.11.2016


 English version:
Journal of Mathematical Sciences (New York), 2018, 229:6, 772–781

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