Skip to main content

On the use of alternating kernels in nonparametric statistical estimation

  • Conference paper
  • First Online:
Probability Theory and Mathematical Statistics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1021))

  • 1579 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Rosenblatt M. Curve estimates.-Ann. Math. Statist., 1971, v.42, No.6, 1815–1842.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bartlett M.S. Statistical estimation of density function.-Sankhya. Indian J.Statistics, Ser. A, 1963, v.25, No.3, 245–254.

    MATH  MathSciNet  Google Scholar 

  3. Alekseev V.G. Some problems in the spectral analysis of Gaussian random processes. — Teoriya Veroyatnist. i Mat. Statist. (Theory Probab. And Math. Statist.), 1974, NO.10, 3–11.

    Google Scholar 

  4. Hannan E.J. Multiple Time Series, N.Y., John Wiley, 1970.

    Book  MATH  Google Scholar 

  5. Palmer D.F. Bias criteria for the selection of spectral windows.-JEEE Trans. Inform. Theory, 1969, v.IT-15, No.5,613–615.

    Article  Google Scholar 

  6. Zhurbenko I.G., Kozhevnikova I.A. On comparative characteristics of the estimates for the spectral density functions of stationary random processes.-Problemy Peredachi Inform. (Probl. Inform. Transmission), 1982, v.18, No.1, 64–77.

    MATH  MathSciNet  Google Scholar 

  7. Alekseev V.G. Some practical recommendations related to spectral analysis of Gaussian stationary random processes.-Problemy Peredachi Inform. (Probl.Inform.Transmission), 1973, v.9, No.4, 42–48.

    MATH  Google Scholar 

  8. Yaglom A.M. Correlation Theory of Stationary Random Functions, Leningrad, Gidrometeoizdat, 1981 (in Russian).

    Google Scholar 

  9. Khachaturova T.V. Spectrum estimate of stationary random processes.--Zapiski Nauchn. Semin. LOMI (Trans. Res. Seminars Leningra Branch Math. Inst. Acad.Sci. USSR), I&72, No.29, 42–50.

    Google Scholar 

  10. Samarov A.M. Lower bound for risk function of spectral density estimates.-Problemy Peredachi Inform. (Probl. Inform. Transmission), 1977, v.13, No.I, 67–72.

    MATH  MathSciNet  Google Scholar 

  11. Alekseev V.G. On the error of estimation of the spectral density function of a Gaussian random process.-Teoriya Veroyatnost.i Mat. Statist. (Theory Probab. and Math. Statist.), 1979, No.21, 3–9.

    Google Scholar 

  12. Gaposkin V.F. Almost surely convergence of the estimates of the spectral density of a stationary process.-Teoriya Veroyatn. i Primen. (Theory Probab. and Appl.), 1980, v.25, No.I,172–178.

    MathSciNet  Google Scholar 

  13. Alekseev V.G. On calculation of the spectra of the stationary random process for large samples.-Problemy Peredachi Inform. (Probl.Inform.Transmission), 1980, v.16, No.I, 42–49.

    MATH  Google Scholar 

  14. Alekseev V.G. On calculation of the spectral densities of the random processes for large samples.-Vychisl. i Prikl. Matem. (Calculating and Applied Mathematics), 1981, No. 44, 32–40.

    Google Scholar 

  15. Koopmans L.H. The Spectral Analysis of Time Series, N.Y., Academic Press, 1974.

    MATH  Google Scholar 

  16. Brillinger D.R. Time Series. Data Analysis and Theory. N.Y., Holt, Rinehart and Winston, 1975.

    MATH  Google Scholar 

  17. Bloomfield P. Fourier Analysis of Time Series: an Introduction. N.Y., John Wiley, 1976.

    MATH  Google Scholar 

  18. Zhurbenko I.G. On spectral density estimations with small dependence on far frequencies.-Teoriya Veroyatnost. i Mat.Statist. (Theory Probab. and Math. Statist.), 1978, No.19, 57–66.

    Google Scholar 

  19. Zhurbenko I.G. On local properties of a spectral density estimate.-Problemy Peredachi Inform. (Probl. Inform. Transmission),1978, v.14, No.3, 85–91.

    MATH  MathSciNet  Google Scholar 

  20. Thomson D.J. Spectrum estimation techniques for characterization and development of WT4 waveguide — I.-Bell System Technical Journ., 1977, v.56, No.9, 1769–1815.

    Google Scholar 

  21. Harris F.J. On the use of windows for harmonic analysis with discrete Fourier transform.-Proc. IEEE, 1978, v.66, No.I, 51–83.

    Article  Google Scholar 

  22. Alekseev V.G., Yaglom A.M. Nonparametric and parametric spectrum estimation methods for stationary time series.-In: Time Series. Proceedings of the International Conference Held at Nottingham University, March 1979. Amsterdam-N.Y.-Oxford, North-Holland, 1980, 401–422.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alekseev, V.G. (1983). On the use of alternating kernels in nonparametric statistical estimation. In: Prokhorov, J.V., Itô, K. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072899

Download citation

  • DOI: https://doi.org/10.1007/BFb0072899

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12718-5

  • Online ISBN: 978-3-540-38701-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics