Estimation Problems for Periodically Correlated Isotropic Random Fields

Iryna Dubovetska, Oleksandr Masyutka and Mikhail Moklyachuk ()
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Iryna Dubovetska: Kyiv National Taras Shevchenko University
Oleksandr Masyutka: Kyiv National Taras Shevchenko University
Mikhail Moklyachuk: Kyiv National Taras Shevchenko University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 41-57

Abstract: Abstract Spectral theory of isotropic random fields in Euclidean space developed by M. I. Yadrenko is exploited to find a solution to the problem of optimal linear estimation of the functional $$ A\zeta ={\sum\limits_{t=0}^{\infty}}\,\,\,{\int_{S_n}} \,\,a(t,x)\zeta (t,x)\,m_n(dx) $$ which depends on unknown values of a periodically correlated (cyclostationary with period T) with respect to time isotropic on the sphere S n in Euclidean space E n random field ζ(t, x), t ∈ Z, x ∈ S n . Estimates are based on observations of the field ζ(t, x) + θ(t, x) at points (t, x), t = − 1, − 2, ..., x ∈ S n , where θ(t, x) is an uncorrelated with ζ(t, x) periodically correlated with respect to time isotropic on the sphere S n random field. Formulas for computing the value of the mean-square error and the spectral characteristic of the optimal linear estimate of the functional Aζ are obtained. The least favourable spectral densities and the minimax (robust) spectral characteristics of the optimal estimates of the functional Aζ are determined for some special classes of spectral densities.

Keywords: Random field; Prediction; Filtering; Robust estimate; Mean square error; Least favourable spectral densities; Minimax spectral characteristic; 60G60; 62M40; 62M20; 93E10; 93E11 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9339-6

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