Construction of a criterion for testing hypotheses about the covariance function of a Gaussian homogeneous isotropic field. (English. Ukrainian original) Zbl 0994.60037

Revenko, A. O.

Theory Probab. Math. Stat. 62, 133-143 (2001); translation from Teor. Jmovirn. Mat. Stat. 62, 124-133 (2000).

This paper deals with the homogeneous and isotropic mean square continuous Gaussian random fields. Estimations for supremum of square-Gaussian random fields are obtained. Further, estimations for the correlation function of the homogeneous and isotropic Gaussian random field are given. And finally, the criterion of hypothesis testing with respect to the covariance function of the Gaussian random field are formulated with the help of estimations for the correlation function.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G07	General theory of stochastic processes
60G60	Random fields
60G15	Gaussian processes
62F03	Parametric hypothesis testing

Keywords:

homogeneous and isotropic Gaussian random field; correlation function; covariance function; hypothesis testing