Scholarlink

<p>Axially symmetric processes, those stationary in longitude but nonstationary across latitude, provide a flexible and physically meaningful class of models for global environmental data. Despite their wide use, the asymptotic properties of classical method-of-moments (MOM) estimators for these processes remain largely unexamined. In this work, we investigate MOM estimators of covariances and cross-variograms for axially symmetric Gaussian processes observed on regular latitude-longitude grids. First, we show that MOM covariance estimators are asymptotically biased. We then examine MOM estimators of cross-variograms, and prove that they are unbiased. However, using the block circulant structure of the covariance matrix and its Fourier diagonalization, we establish MOM cross-variogram estimators are not consistent. These findings illustrate intrinsic limitations of MOM-type estimators on compact manifolds and emphasize that Euclidean intuition does not carry over to spherical settings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Note on Asymptotics of Estimators for Axially Symmetric Processes on the Sphere

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月12日

查看全文
  • Haimeng Zhang,
  • Chunfeng Huang,
  • Xiaohuan Xue,
  • A. L. A. R. R. Thanuja,
  • Bukola O. Adaramola

摘要

Axially symmetric processes, those stationary in longitude but nonstationary across latitude, provide a flexible and physically meaningful class of models for global environmental data. Despite their wide use, the asymptotic properties of classical method-of-moments (MOM) estimators for these processes remain largely unexamined. In this work, we investigate MOM estimators of covariances and cross-variograms for axially symmetric Gaussian processes observed on regular latitude-longitude grids. First, we show that MOM covariance estimators are asymptotically biased. We then examine MOM estimators of cross-variograms, and prove that they are unbiased. However, using the block circulant structure of the covariance matrix and its Fourier diagonalization, we establish MOM cross-variogram estimators are not consistent. These findings illustrate intrinsic limitations of MOM-type estimators on compact manifolds and emphasize that Euclidean intuition does not carry over to spherical settings.