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.

翻译：本文研究了两种高斯矩张量估计器：标准样本矩估计器以及基于Isserlis定理的插件估计器。我们建立了与维度无关的非渐近误差界，这些误差界展示并量化了Isserlis估计器在偶数阶$p>2$张量上的优势。我们的误差界在算子和逐项最大范数下均成立，并适用于对称和非对称张量。