ABSTRACT We study the asymptotic behaviour of least squares estimators (LSE) in regression models for long-range dependent random fields observed on spheres. The LSE 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.

中文翻译：

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球体上长程相关随机场回归模型中的 LSE

摘要 我们研究了在球体上观察到的长程相关随机场的回归模型中最小二乘估计量 (LSE) 的渐近行为。LSE 可以作为远程相关随机场的加权函数给出。众所周知，在这种情况下，限制可以是非高斯的。我们推导出估计器的极限分布和相应的收敛速度。结果是在对随机场的相当笼统的假设下获得的。进行了模拟研究以支持理论发现。