{"ID":2891893,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16734","arxiv_id":"2507.16734","title":"Testing and estimation in orthosymmetric Gaussian sequence model","abstract":"We study the Gaussian sequence model, i.e. $X \\sim N(\\mathbfθ, I_\\infty)$, where $\\mathbfθ \\in Γ\\subset \\ell_2$ is assumed to be convex and compact. We show that goodness-of-fit testing sample complexity is lower bounded by the square-root of the estimation complexity, whenever $Γ$ is orthosymmetric. This lower bound is tight when $Γ$ is also quadratically convex (as shown by [Donoho et al. 1990, Neykov 2023]). We also completely characterize likelihood-free hypothesis testing (LFHT) complexity for $\\ell_p$-bodies, discovering new types of tradeoff between the numbers of simulation and observation samples, compared to the case of ellipsoids (p = 2) studied in [Gerber and Polyanskiy 2024].","short_abstract":"We study the Gaussian sequence model, i.e. $X \\sim N(\\mathbfθ, I_\\infty)$, where $\\mathbfθ \\in Γ\\subset \\ell_2$ is assumed to be convex and compact. We show that goodness-of-fit testing sample complexity is lower bounded by the square-root of the estimation complexity, whenever $Γ$ is orthosymmetric. This lower bound i...","url_abs":"https://arxiv.org/abs/2507.16734","url_pdf":"https://arxiv.org/pdf/2507.16734v4","authors":"[\"Zeyu Jia\",\"Yury Polyanskiy\"]","published":"2025-07-22T16:20:57Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"cs.IT\"]","methods":"[]","has_code":false}