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arXiv · 2507.06166

On the Estimation of Gaussian Moment Tensors

Omar Al-Ghattas·Jiaheng Chen·Daniel Sanz-Alonso
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Abstract

This paper studies two estimators for Gaussian moment tensors: the standard sample moment estimator and a plug-in estimator based on Isserlis's theorem. We establish dimension-free, non-asymptotic error bounds that demonstrate and quantify the advantage of Isserlis's estimator for tensors of even order $p>2$. Our bounds hold in operator and entrywise maximum norms, and apply to symmetric and asymmetric tensors.

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Omar Al-Ghattas, Jiaheng Chen, Daniel Sanz-Alonso. 2025-07-08. On the Estimation of Gaussian Moment Tensors. https://arxiv.org/abs/2507.06166

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