On LSE in regression model for long-range dependent random fields on spheres

Abstract: We study the asymptotic behaviour of least squares estimators in regression models for long-range dependent random fields observed on spheres. The least squares estimator can be given as a weighted functional of long-range dependent random fields. It is known that in this scenario the limits can be non-Gaussian. We derive the limit distribution and the corresponding rate of convergence for the estimators. The results were obtained under rather general assumptions on the random fields. Simulation studies were conducted to support theoretical findings.