Skip to main content
SpringerLink
Log in
Book cover

Modern Stochastics and Applications pp 319–336Cite as

Minimum Contrast Method for Parameter Estimation in the Spectral Domain

  • Chapter
  • First Online:

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 90))

Abstract

We provide a concise summary on the method of parameter estimation of random fields in the spectral domain developed in the papers [1–3], which is based on higher-order information and the minimum contrast principle. The exposition covers both continuous and discrete-time cases. Minimum contrast estimators are defined via minimization of a certain empirical spectral functional of kth order based on tapered data. Conditions for consistency and asymptotic normality of the estimators are stated.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Quasilikelihood-based higher-order spectral estimation of random processes and fields with possible long-range dependence. J. Appl. Probab. 41A, 35–54 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Minimum contrast estimation of random processes based on information of second and third orders. J. Statist. Plann. Inference. 137, 1302–1331 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Statistical inference using higher-order information. J. Multivariate Anal. 98(4), 706–742 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Evaluation of bias in higher-order spectral estimation. Probab. Theory and Math. Stat. 80, 1–14 (2009)

    Article  Google Scholar 

  5. Avram, F., Leonenko, N., Sakhno, L.: On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM Probab. Stat. 14, 210–255 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bentkus, R.: On the error of the estimate of the spectral function of a stationary process. Liet. Mat. Rink. 12, 55–71 (1972, in Russian)

    Google Scholar 

  7. Brillinger, D.R.: The frequency analysis of relations between stationary spatial series. In: Proceedings of the 12th Biennial Seminar of the Canadian Mathematical Congress, Montreal, pp. 39–81 (1970)

    Google Scholar 

  8. Brillinger, D.R., Rosenblatt, M.: Asymptotic theory of estimates of k-th order spectra. In: Harris, B. (ed.) Spectral Analysis Time Series, pp. 153–188. Wiley, New York (1967)

    Google Scholar 

  9. Dahlhaus, R.: Spectral analysis with tapered data. J. Time. Ser. Anal. 4, 163–175 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  10. Guyon, X.: Random Fields on a Network: Modelling, Statistics and Applications. Springer, New York (1995)

    MATH  Google Scholar 

  11. Ibragimov, I.A.: On maximum likelihood estimation of parameters of the spectral density of stationary time series. Theor. Prob. Appl. 12, 115–119 (1967)

    Article  Google Scholar 

  12. Taniguchi, M.: Minimum contrast estimation for spectral densities of stationary processes. J. R. Stat. Soc., Ser. B. 49, 315–325 (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, 64 Volodymyrska, 01601, Kyiv, Ukraine

    Lyudmyla Sakhno

Authors
  1. Lyudmyla Sakhno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lyudmyla Sakhno .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Volodymyr Korolyuk

  2. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, Compiegne Cedex, France

    Nikolaos Limnios

  3. Dept. of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuliya Mishura

  4. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Lyudmyla Sakhno

  5. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Georgiy Shevchenko

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sakhno, L. (2014). Minimum Contrast Method for Parameter Estimation in the Spectral Domain. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_18

Download citation

Publish with us

Policies and ethics

Search

Navigation