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The problem of estimation of unknown mean value for some correlation models of homogeneous and isotropic random fields
Author(s):
M.
I.
Yadrenko;
N.
Semenovs'ka
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
193-201.
MSC (2000):
Primary 60J60, 60J12, 60J25
Posted:
September 6, 2006
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Additional information
Abstract:
We obtain explicit formulas for the variance of a linear unbiased estimator of unknown mean value for some correlation models of homogeneous and isotropic random fields.
References:
-
- 1.
- M. I. Yadrenko, Spectral Theory of Random Fields, ``Vyshcha shkola'', Kiev, 1980; English transl., Optimization Software, Inc., Publications Division, New York, 1983. MR 0697386 (84f:60003)
- 2.
- N. Semenovs'ka and M. I. Yadrenko, Explicit extrapolation formulas for some correlation models of homogeneous and isotropic random fields, Teor. Imovirnost. Matem. Statist. 69 (2003), 162-171; English transl. in Theory Probab. Math. Statist. 69 (2004), 175-185. MR 2110915 (2005k:60160)
- 3.
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 -dimensional space similar to stationary stochastic processes, Teor. Veroyatnost. i Primenen. 2 (1957), no. 3, 292-338. (Russian) MR 0094844 (20:1353) - 4.
- C. E. Buell, Correlation functions for wind and geopotential on isobaric surfaces, J. Appl. Meteorology 11 (1972), 51-59.
- 5.
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- 6.
- M. I. Yadrenko, Some statistical problems for the Whittle random processes, Teor. Imovirnost. Matem. Statist. 63 (2000), 163-167; English transl. in Theory Probab. Math. Statist. 63 (2001), 179-183. MR 1870787 (2002m:60097
- 7.
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- 8.
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- -, Higher Transcendental Functions, vol. 2, McGraw-Hill Book Company, New York-Toronto-London, 1953. MR 0058756 (15:419i)
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- M. I. Yadrenko, Isotropic random fields of Markov type in Euclidean and Hilbert spaces, Proc. All-Union Conf. Theory Prob. and Math. Statist. (Erevan, 1958), Izdat. Akad. Nauk Armjan. SSR, Erevan, 1960, 263-285. (Russian) MR 0214123 (35:4974)
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Additional Information:
M.
I.
Yadrenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
N.
Semenovs'ka
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
semenovsky@hotmail.ru
DOI:
10.1090/S0094-9000-06-00676-4
PII:
S 0094-9000(06)00676-4
Keywords:
Random field,
Whittle--Mattern model,
linear unbiased model
Received by editor(s):
5/JUN/2004
Posted:
September 6, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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