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Asymptotic properties of the method of observed mean for homogeneous random fields

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Abstract

The empirical estimate of the unknown parameter of a homogenous (in restricted sense) random field with continuous time and continuous states observed in a circle is considered. The strong consistency of the estimate is proved. The conditions under which the estimates weakly converge to the Gaussian distribution are established.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    D. A. Gololobov

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

    E. J. Kasitskaya

Authors
  1. D. A. Gololobov
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  2. E. J. Kasitskaya
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Corresponding author

Correspondence to D. A. Gololobov.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2013, pp. 160–167.

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Gololobov, D.A., Kasitskaya, E.J. Asymptotic properties of the method of observed mean for homogeneous random fields. Cybern Syst Anal 49, 465–471 (2013). https://doi.org/10.1007/s10559-013-9530-3

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  • DOI: https://doi.org/10.1007/s10559-013-9530-3

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