Testing Diagonal Anisotropy Based on Single Realisation of Spherical Random Field
Abstract
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.
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BibTeX
@misc{khan2026testing,
title = {{Testing Diagonal Anisotropy Based on Single Realisation of Spherical Random Field}},
author = {Shahid Khan and Andriy Olenko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36786},
eprint = {2609.36786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36786},
}
RIS
TY - UNPB
TI - Testing Diagonal Anisotropy Based on Single Realisation of Spherical Random Field
AU - Shahid Khan
AU - Andriy Olenko
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.36786
UR - https://arxiv.org/abs/2609.36786
AB - 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.
ER -