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On an estimator for the unknown mean of a homogeneous random field of a discrete argument. (English. Russian original) Zbl 0699.60035

Theory Probab. Math. Stat. 40, 159-166 (1990); translation from Teor. Veroyatn. Mat. Stat., Kiev 40, 132-140 (1989).
Summary: A study is made of the behavior of the arithmetic mean estimator of the mean value of a homogeneous random field of a discrete argument, observed on a “cross”. Attention is directed to the way in which the zeros in the spectrum of the field influence the asymptotic behavior of the variance of the estimator. Examples are considered. The variance of the arithmetic mean estimator is computed for a series of concrete spectral densities.

MSC:

60G60 Random fields
62G05 Nonparametric estimation
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