This analysis reveals dimensional dependence in assessing gaussianity using the Hermite method, suggesting new insights into statistical testing.
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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Basse-O’Connor et al. (2025) studied this question.
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