A lower bound for minimax risk is constructed for the problem of estimating an unknown pseudoperiodic function observed in Gaussian stationary noise with spectral density satisfying some version of the Muckenhoupt condition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. A. Rozanov, Stationary Processes [in Russian], Moscow (1963).
I. A. Ibragimov and Yu. A. Rozanov, Gaussian Processes [in Russian], Moscow (1974).
D. L. Donoho, R. C. Liu, and B. MacGibbon, “Minimax risk over hyperrectangles, and implications,” Ann. Statist., 18, No. 3, 1416–1437 (1990).
W. Stepanoff, “Sur quelques generalisations des fonctions presque-periodiques,” Comptes Rendus, 181, 90–92 (1925).
R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain [Russian translation], Moscow (1964).
J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).
V. N. Solev, “A condition for the local asymptotic normality of Gaussian stationary processes,” Zap. Nauchn. Semin. POMI, 278, 225–247 (2001).
V. N. Solev, “Estimation of function observed in stationary noise: discretization,” Zap. Nauchn. Semin. POMI, 441, 286–298 (2015).
V. N. Solev, “Adaptive estimation of a function observed in Gaussian stationary noise,” Zap. Nauchn. Semin. POMI, 454, 261–275 (2016).
V. N. Solev, “A local version of the Muckenhoupt condition and the accuracy of estimation of the unknown pseudo periodic function in stationary noise,” Zap. Nauchn. Semin. POMI, 466, 261–275 (2017).
V. N. Solev, “Estimation of function in Gaussian stationary noise: new spectral condition,” Zap. Nauchn. Semin. POMI, 486, 275–285 (2018).
V. N. Solev, “Estimation of a function in a Gaussian stationary noise,” Zap. Nauchn. Semin. POMI, 495, 277–290 (2020).
S. V. Reshetov, “Minimax risk for quadratically convex sets,” Zap. Nauchn. Semin. POMI, 368, 181–189 (2009).
S. V. Reshetov, “The minimax estimator of the pseudo-periodic function observed in the stationary noise,” Vestn. SPbGU, Ser. 1, 2, 106–115 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 505, 2021, pp. 282–293.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Solev, V.N. A Lower Bound for Minimax Risk in a Problem of Estimating a Function in Stationary Gaussian Noise. J Math Sci 281, 196–204 (2024). https://doi.org/10.1007/s10958-024-07085-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-024-07085-1