On estimators of the correlation and spectral functions of a homogeneous and isotropic Gaussian random field. (English. Russian original) Zbl 0634.62093

Dykhovichnyj, A. A.

Theory Probab. Math. Stat. 32, 17-26 (1986); translation from Teor. Veroyatn. Mat. Stat. 32, 17-27 (1985).

Summary: Estimators for the correlation function of a homogeneous and isotropic Gaussian random field from observations on a sphere and the associated estimators of the spectral function are considered. Unbiasedness and consistency are proved. Assertions are obtained about the asymptotic normality of the estimators and weak convergence of the measures induced by the estimator of the correlation function to a Gaussian measure on the space of the continuous functions.

MSC:

62M99	Inference from stochastic processes
62M15	Inference from stochastic processes and spectral analysis
62E20	Asymptotic distribution theory in statistics
60B10	Convergence of probability measures
60F05	Central limit and other weak theorems
60G60	Random fields
62F12	Asymptotic properties of parametric estimators
62M09	Non-Markovian processes: estimation

Keywords:

homogeneous and isotropic Gaussian random field; observations on a sphere; estimators of the spectral function; Unbiasedness; consistency; asymptotic normality; weak convergence; estimator of the correlation function