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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(x1, ···, 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.

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