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This is a Quantitative Study study.

October 7, 2025Open Access

Exponential dimensional dependence in high-dimensional Hermite method of moments

Key Points

Exponential dimensional dependence indicates significance in the Hermite method of moments.
The research establishes bounds for Kolmogorov-Smirnov and convex distances in high-dimensional settings.
Analysis focuses on i.i.d. Gaussian variables, emphasizing the method's applicability in statistical tests.
Findings support improved statistical testing methodologies for complex high-dimensional data.

Abstract

In this paper, we show exponential dimensional dependence for the Hermite method of moments as a statistical test for Gaussianity in the case of i.i.d. Gaussian variables, by constructing a lower bound for the the Kolmogorov-Smirnov distance and an upper bound for the convex distance.

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Cite This Study

Basse-O’Connor et al. (Thu,) studied this question.

synapsesocial.com/papers/68e585d0b1e78cc4e5f4646b https://doi.org/https://doi.org/10.48550/arxiv.2502.17431

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