PreprintCC BY 4.0arXiv
Applications of Royen's Gaussian Correlation Inequality in high-dimensional testing
Abstract
Royen's Gaussian Correlation Inequality (GCI) is a fundamental result in statistics and probability, but unfortunately, at least by now, the result is not very well known in the statistical community. In this paper, we demonstrate the potential of GCI in high-dimensional testing problems that involve multivariate Gaussian variables. Leveraging the GCI, we establish sharp Type I error bounds under arbitrary Gaussian covariance structures. We also formulate a conjecture and relate it to the well-known Spherical Cap Covering Conjecture in discrete geometry and Weak Simplex Conjecture in information theory.
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BibTeX
@misc{jin2026applications,
title = {{Applications of Royen's Gaussian Correlation Inequality in high-dimensional testing}},
author = {Jiashun Jin and Zheng Tracy Ke and Jingming Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15188},
eprint = {2610.15188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15188},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Applications of Royen's Gaussian Correlation Inequality in high-dimensional testing
AU - Jiashun Jin
AU - Zheng Tracy Ke
AU - Jingming Wang
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15188
UR - https://arxiv.org/abs/2610.15188
AB - Royen's Gaussian Correlation Inequality (GCI) is a fundamental result in statistics and probability, but unfortunately, at least by now, the result is not very well known in the statistical community. In this paper, we demonstrate the potential of GCI in high-dimensional testing problems that involve multivariate Gaussian variables. Leveraging the GCI, we establish sharp Type I error bounds under arbitrary Gaussian covariance structures. We also formulate a conjecture and relate it to the well-known Spherical Cap Covering Conjecture in discrete geometry and Weak Simplex Conjecture in information theory.
ER -