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A note on the estimation of the mean of a homogeneous random field

Published online by Cambridge University Press:  14 July 2016

Michael Skalsky
Michael Skalsky*
Affiliation:
Southern Illinois University
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Extract

An important problem, arising in connection with the estimation of mathematical expectation of a homogeneous random field X(x 1, ···, xn ) in Rn by means of the arithmetic mean of observed values, is to determine the number of observations for which the variance of the estimate attains its minimum. Vilenkin [2] has shown, that in the case of a stationary random process X(x) such a finite number exists, provided that the covariance function satisfies certain conditions.

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 8 , Issue 3 , September 1971 , pp. 626 - 629
Copyright
Copyright © Applied Probability Trust 1971 

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References

[1] Davidovich, Yu. S. and Kartashov, Yu. V. (1968) On the estimation of a mean of the homogenous random fields. Visnik Kiiv Univ. No. 10, Ser. Mat. Mech. 119–123.Google Scholar
[2] Vilenkin, S. Ya. (1959) On the estimation of the mean in stationary processes. Theor. Probability Appl. 4, 415–416.CrossRefGoogle Scholar