{"ID":2897160,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.06166","arxiv_id":"2507.06166","title":"On the Estimation of Gaussian Moment Tensors","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 $p\u003e2$. Our bounds hold in operator and entrywise maximum norms, and apply to symmetric and asymmetric tensors.","short_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 $p\u003e2$. Our bound...","url_abs":"https://arxiv.org/abs/2507.06166","url_pdf":"https://arxiv.org/pdf/2507.06166v2","authors":"[\"Omar Al-Ghattas\",\"Jiaheng Chen\",\"Daniel Sanz-Alonso\"]","published":"2025-07-08T16:46:41Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}