Least squares estimation of regression coefficients of singular random fields observed on a sphere (Q2746396)

A continuous-parameter homogeneous isotropic random field is called singular if its covariances decrease to zero at infinity but their integral diverges. An alternative definition is available via Tauberian-Abelian theorems, which requires the spectral density to be unbounded at the origin. Such processes arise in hydrology, meteorology, turbulence theory etc. This paper investigates regression models for homogeneous and isotropic random fields observed on a sphere of an increasing radius. Models with singular random noise are considered. Results on the rate of convergence to the normal law of the least squares estimates are presented.