Advertisement

Journal of Mathematical Sciences

, Volume 244, Issue 5, pp 896–902 | Cite as

A Local Version of the Muckenhoupt Condition and the Accuracy of Estimation of an Unknown Pseudoperiodic Function in Stationary Noise

  • V. N. SolevEmail author
Article
  • 1 Downloads

In this paper, we construct lower and upper bounds of the minimax risk in the estimation problem when we observe the unknown pseudoperiodic function in stationary noise with density satisfying a local version of the Muckenhoupt condition.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. A. Rozanov, Stationary Processes [in Russian], Moscow (1963).Google Scholar
  2. 2.
    I. A. Ibragimov and Yu. A. Rozanov, Gaussian Processes [in Russian], Moscow (1974).Google Scholar
  3. 3.
    I. A. Ibragimov and R. Z. Khas’minskii, “Nonparametric estimation of the value of a linear functional in Gaussian white noise,” Teor. Veroyatn. Primen., 29, 19–32 (1984).MathSciNetGoogle Scholar
  4. 4.
    W. Stepanoff, “Sur quelques generalisations des fonctions presque-periodiques,” Comptes Rendus, 181, 90–92 (1925).zbMATHGoogle Scholar
  5. 5.
    R. E. A. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain [Russian translation], Moscow (1964).Google Scholar
  6. 6.
    J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).zbMATHGoogle Scholar
  7. 7.
    S. V. Reshetov, “The minimax estimator of the pseudoperiodic function obversed in the stationary roise,” Vestnik St.Petersb. Univ. Mat., 43, 106–115 (2010).MathSciNetGoogle Scholar
  8. 8.
    V. N. Solev, “A condition for the local asymptotic normality of Gaussian stationary processes,” Zap. Nauchn. Semin. POMI, 278, 225–247 (2001).Google Scholar
  9. 9.
    V. N. Solev, “Adaptive estimation of a function observed on a background of Gaussian stationary noise,” Zap. Nauchn. Semin. POMI, 454, 261–275 (2016).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations