A theorem on estimating the mean of a stationary random field. (English. Russian original) Zbl 0788.62086

Shilo, L. V.

Theory Probab. Math. Stat. 44, 135-139 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 44, 135-140 (1991).

Summary: An investigation is made of the asymptotic behavior of the variance of the arithmetic mean estimator of the unknown mean of a homogeneous random field that can be observed on the domain \(K_ T=\{(m,n): | m|+ | n|\leq T;\;m,\;n,\;T\in Z\}\). The concrete results relate to the case when the spectral density of the field vanishes at the origin of the coordinate system.

MSC:

62M40	Random fields; image analysis
62G05	Nonparametric estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

arithmetic mean estimator; homogeneous random field; spectral density