The problem of estimation of unknown mean value for some correlation models of homogeneous and isotropic random fields. (Ukrainian, English) Zbl 1121.62084

Yadrenko, M. I.; Semenovs’ka, N.

Teor. Jmovirn. Mat. Stat. 72, 172-179 (2005); translation in Theory Probab. Math. Stat. 72, 193-201 (2006).

Let \(\xi(x),x\in\mathbb R^n\), be a homogeneous and isotropic random field with the correlation function \(E\xi(x)\xi(y)=\varphi(r), r=| x-y| \). For these random fields with correlation functions from the C. E. Buell [J. Appl. Meteorology, 11, 51-59 (1972)] list of correlation functions the authors obtain explicit formulas for computation of the least squares means linear estimates (and the mean square errors) of the unknown expectation \(E\xi(x)=a\) of the field. For more results see N. V. Semenovs’ka and M. I. Yadrenko [Teor. Jmovirn. Mat. Stat. 69, 162-171 (2004); translation in Theory Probab. Math. Stat. 69, 175-185 (2004; Zbl 1097.60038)].

Reviewer: Mikhail P. Moklyachuk (Kyïv)

MSC:

62M40	Random fields; image analysis
60G60	Random fields

Keywords:

homogeneous isotropic random field; correlation model

Citations:

Zbl 1097.60038