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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