caa a22 4500 605519447 CHVBK 20210128100730.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s11009-013-9339-6 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9339-6 Estimation Problems for Periodically Correlated Isotropic Random Fields [Elektronische Daten] Estimation Problems for Random Fields [Iryna Dubovetska, Oleksandr Masyutka, Mikhail Moklyachuk] 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. Springer Science+Business Media New York, 2013 Random field nationallicence Prediction nationallicence Filtering nationallicence Robust estimate nationallicence Mean square error nationallicence Least favourable spectral densities nationallicence Minimax spectral characteristic nationallicence Dubovetska Iryna Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut Masyutka Oleksandr Department of Mathematics and Theoretical Radiophysics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut Moklyachuk Mikhail Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 41-57 1387-5841 17:1<41 2015 17 11009 https://doi.org/10.1007/s11009-013-9339-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9339-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dubovetska Iryna Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Masyutka Oleksandr Department of Mathematics and Theoretical Radiophysics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Moklyachuk Mikhail Department of Probability Theory, Statistics and Actuarial Mathematics, Kyiv National Taras Shevchenko University, 01601, Kyiv, Ukraine aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/1(2015-03-01), 41-57 1387-5841 17:1<41 2015 17 11009