Testing and estimation in orthosymmetric Gaussian sequence model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909879262773248 |
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| author | Jia, Zeyu Polyanskiy, Yury |
| author_facet | Jia, Zeyu Polyanskiy, Yury |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Testing and estimation in orthosymmetric Gaussian sequence model Jia, Zeyu Polyanskiy, Yury Statistics Theory Information Theory 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]. |
| title | Testing and estimation in orthosymmetric Gaussian sequence model |
| topic | Statistics Theory Information Theory |
| url | https://arxiv.org/abs/2507.16734 |