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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2603.25280 |
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| _version_ | 1866917362923470848 |
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| author | Zlatanov, Nikola Gohari, Amin Shahrivari, Farzad Rudakov, Mikhail |
| author_facet | Zlatanov, Nikola Gohari, Amin Shahrivari, Farzad Rudakov, Mikhail |
| contents | Classical estimation outputs a single point estimate of an unknown $d$-dimensional vector from an observation.
In this paper, we study \emph{$k$-list estimation}, in which a single observation is used to produce a list of $k$ candidate estimates and performance is measured by the expected squared distance from the true vector to the closest candidate. We compare this centralized setting with a symmetric decentralized MMSE benchmark in which $k$ agents observe conditionally i.i.d.\ measurements and each agent outputs its own MMSE estimate. On the centralized side, we show that optimal $k$-list estimation is equivalent to fixed-rate $k$-point vector quantization of the posterior distribution and, under standard regularity conditions, admits an exact high-rate asymptotic expansion with explicit constants and decay rate $k^{-2/d}$. On the decentralized side, we derive lower bounds in terms of the small-ball behavior of the single-agent MMSE error; in particular, when the conditional error density is bounded near the origin, the benchmark distortion cannot decay faster than order $k^{-2/d}$. We further show that if the error density vanishes at the origin, then the decentralized benchmark is provably unable to match the centralized $k^{-2/d}$ exponent, whereas the centralized estimator retains that scaling. Gaussian specializations yield explicit formulas and numerical experiments corroborate the predicted asymptotic behavior. Overall, the results show that, in the scaling with $k$, one observation combined with $k$ carefully chosen candidates can be asymptotically as effective as -- and in some regimes strictly better than -- this MMSE-based decentralized benchmark with $k$ independent observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25280 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | List Estimation Zlatanov, Nikola Gohari, Amin Shahrivari, Farzad Rudakov, Mikhail Information Theory Statistics Theory Classical estimation outputs a single point estimate of an unknown $d$-dimensional vector from an observation. In this paper, we study \emph{$k$-list estimation}, in which a single observation is used to produce a list of $k$ candidate estimates and performance is measured by the expected squared distance from the true vector to the closest candidate. We compare this centralized setting with a symmetric decentralized MMSE benchmark in which $k$ agents observe conditionally i.i.d.\ measurements and each agent outputs its own MMSE estimate. On the centralized side, we show that optimal $k$-list estimation is equivalent to fixed-rate $k$-point vector quantization of the posterior distribution and, under standard regularity conditions, admits an exact high-rate asymptotic expansion with explicit constants and decay rate $k^{-2/d}$. On the decentralized side, we derive lower bounds in terms of the small-ball behavior of the single-agent MMSE error; in particular, when the conditional error density is bounded near the origin, the benchmark distortion cannot decay faster than order $k^{-2/d}$. We further show that if the error density vanishes at the origin, then the decentralized benchmark is provably unable to match the centralized $k^{-2/d}$ exponent, whereas the centralized estimator retains that scaling. Gaussian specializations yield explicit formulas and numerical experiments corroborate the predicted asymptotic behavior. Overall, the results show that, in the scaling with $k$, one observation combined with $k$ carefully chosen candidates can be asymptotically as effective as -- and in some regimes strictly better than -- this MMSE-based decentralized benchmark with $k$ independent observations. |
| title | List Estimation |
| topic | Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2603.25280 |