发表机构
La Trobe University（拉筹伯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对球面随机场单一实现场景，提出得分检验和累积和型检验以检验各向同性对对角各向异性，并通过模拟及普朗克数据验证其性能。
AI 中文摘要
球面数据出现在各种应用中，包括宇宙学和地球科学。此类数据的标准统计模型采用各向同性球面随机场。对于许多现实世界的数据集，各向同性假设可能不切实际。此外，在宇宙学等各类应用中，通常仅观测到该场的一次实现，这使得通过重复采样来评估各向同性变得不可能。本文考虑一种替代的各向异性模型，称为对角各向异性。为了检验各向同性相对于对角各向异性，我们开发了得分检验和累积和型检验。建立了它们的渐近性质，并提出了适用于中等样本量的基于蒙特卡洛的替代方法。通过数值研究，包括对模拟数据和实际普朗克宇宙微波背景辐射观测的应用，展示了所提出方法的性能。这些检验还应用于三张普朗克SMICA宇宙微波背景辐射图，并展示了不同数据发布和地图构建程序如何导致结果变化。
英文摘要
Spherical data appear in various applications, including cosmology and the Earth sciences. A standard statistical model for such data employs isotropic spherical random fields. The isotropy assumption may be unrealistic for many real-world datasets. Also, in various applications such as cosmology, only a single realisation of the field is observed, making isotropy impossible to assess through repeated sampling. This paper considers an alternative anisotropic model, referred to as diagonal anisotropy. To test isotropy against diagonal anisotropy, we develop score and cumulative-sum-type tests. Their asymptotic properties and Monte Carlo-based alternatives suitable for moderate sample sizes are established. The performance of the proposed methods is illustrated by numerical studies via applications to simulated data and to actual Planck cosmic microwave background radiation observations. The tests are also applied to three Planck SMICA cosmic microwave background radiation maps and demonstrate how results can vary for different data releases and map construction procedures.
Comments23 pages, 7 images
