On an estimation of an unknown mean of a homogeneous and isotropic random field observed in an annulus. (English. Ukrainian original) Zbl 0985.60054

Bektashov, S.

Theory Probab. Math. Stat. 61, 1-2 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 1-2 (2000).

This note deals with the homogeneous and isotropic random field \(\xi(r,\varphi)=\alpha+\eta(r,\varphi)\) which is observed at points of the ring \(R_{1}\leq r\leq R_{2}.\) The arithmetic mean estimation is considered as an estimation of the unknown expectation of this field. To obtain the variance of this expectation the spectral representation of this field is used. Asymptotical behaviour of the variance of the arithmetic mean estimation by observations of the field in the ring is considered.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G60	Random fields
62F12	Asymptotic properties of parametric estimators
62M40	Random fields; image analysis

Keywords:

random field; mean-arithmetic estimation; spectral representation