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

## TL;DR

This paper investigates the asymptotic behavior of least squares estimators in regression models involving long-range dependent random fields on spheres, deriving their limit distributions and convergence rates.

## Contribution

It provides the first derivation of limit distributions and convergence rates for LSEs in long-range dependent random fields on spheres under general conditions.

## Key findings

- Limit distributions can be non-Gaussian.
- Convergence rates are explicitly derived.
- Simulation studies support theoretical results.

## 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.