Upper bounds are constructed for minimax risk in the problem of estimating the unknown pseudoperiodic vector function observed against the background of stationary Gaussian noise with spectral density that satisfies the local version of the Muckenhoupt condition.
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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. Sem. POMI, 441, 286–298 (2015)
V. N. Solev, “Adaptive estimation of a function observed on a background of 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).
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 pseudoperiodic function obversed in the stationary roise,” Vestnik St.Petersb. Univ. Mat., 43, 106–115 (2010).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 277–290.
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Solev, V.N. Estimation of a Function in a Gaussian Stationary Noise. J Math Sci 268, 711–720 (2022). https://doi.org/10.1007/s10958-022-06241-9
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DOI: https://doi.org/10.1007/s10958-022-06241-9