Asymptotic efficiency of the arithmetic-mean estimator of the unknown mean of a homogeneous random field

We consider the estimation of the unknown mean of a homogeneous random field from observations on a system of homothetically expanding regions. We examine the asymptotic behavior of the variance of the arithmetic-mean estimator. The arithmetic-mean estimator is shown to be asymptotically efficient in the class of linear estimators.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 106–111, 1988.