Skip to main content
SpringerLink
Log in

Consistency and Properties of Large Deviations of Empirical Estimates in Stochastic Optimization Problems for Homogeneous Random Fields under Nonhomogeneous and Homogeneous Observations

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The paper considers a stochastic programming problem with the empirical function constructed from nonhomogeneous observations of a homogeneous random field. The field satisfying the strong mixing condition is investigated in the problem. The conditions whereby the empirical estimate is consistent are given, and large deviations of the estimate for homogeneous observations are estimated.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. S. Mikhalevich, P. S. Knopov, and A. N. Golodnikov, “Mathematical models and methods of risk assessment in ecologically hazardous industries,” Cybern. Syst. Analysis, Vol. 30, No. 2, 259–273 (1994). https://doi.org/10.1007/BF02366429

    Article  MATH  Google Scholar 

  2. P. S. Knopov and E. J. Kasitskaya, “Properties of empirical estimates in stochastic optimization and identification problems programming problems,” Annals of Oper. Research, Vol. 56, No. 1, 225–239 (1995).

    Article  MathSciNet  Google Scholar 

  3. P. S. Knopov, “Asymptotic properties of some classes of M-estimates,” Cybern. Syst. Analysis, Vol. 33, No. 4, 468–481 (1997). https://doi.org/10.1007/BF02733103.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. S. Knopov and E. J. Kasitskaya, “On large deviations of empirical estimates in a stochastic programming problem with time-dependent observations,” Cybern. Syst. Analysis, Vol. 46, No. 5, 724–728 (2010). https://doi.org/10.1007/s10559-010-9253-7.

    Article  MathSciNet  MATH  Google Scholar 

  5. N. N. Leonenko, “Estimates of linear regression coefficients on a homogeneous random field,” Ukr. Math. J., Vol. 30, No. 6, 562–568 (1978).

    Article  Google Scholar 

  6. A. V. Ivanov and N. N. Leonenko, Statistical Analysis of Random Fields, Kluwer Academic Publ., Dordrecht (1989).

    Book  Google Scholar 

  7. P. S. Knopov, Optimal Estimates of Parameters of Stochastic Systems [in Russian], Naukova Dumka, Kyiv (1981).

    MATH  Google Scholar 

  8. J.-D. Deuscel and D. W. Stroock, Large Deviations, Academ. Press, Boston (1989).

    Google Scholar 

  9. N. Dunford and J. Schwartz, Linear Operators, Pt. I: General Theory, Interscience, New York (1957).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    P. S. Knopov & E. J. Kasitskaya

Authors
  1. P. S. Knopov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. J. Kasitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. S. Knopov.

Additional information

The study was financially supported by the grant 2020.02/0121 of the National Research Foundation of Ukraine.

Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2021, pp. 21–34.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Knopov, P.S., Kasitskaya, E.J. Consistency and Properties of Large Deviations of Empirical Estimates in Stochastic Optimization Problems for Homogeneous Random Fields under Nonhomogeneous and Homogeneous Observations. Cybern Syst Anal 57, 16–29 (2021). https://doi.org/10.1007/s10559-021-00326-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-021-00326-0

Keywords

Search

Navigation