List Estimation
Nikola Zlatanov, Amin Gohari, Farzad Shahrivari, and Mikhail Rudakov

TL;DR
This paper introduces and analyzes $k$-list estimation, comparing centralized and decentralized approaches, and shows that with proper design, list estimation can asymptotically outperform decentralized MMSE benchmarks in high-dimensional settings.
Contribution
It establishes the equivalence of optimal $k$-list estimation to vector quantization of the posterior and derives precise asymptotic decay rates, highlighting advantages over decentralized methods.
Findings
Optimal $k$-list estimation matches vector quantization of the posterior.
Asymptotic decay rate of $k^{-2/d}$ for centralized estimation.
Decentralized benchmarks cannot always match the centralized decay rate.
Abstract
Classical estimation outputs a single point estimate of an unknown -dimensional vector from an observation. In this paper, we study \emph{-list estimation}, in which a single observation is used to produce a list of 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 agents observe conditionally i.i.d.\ measurements and each agent outputs its own MMSE estimate. On the centralized side, we show that optimal -list estimation is equivalent to fixed-rate -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 . On the decentralized side, we derive lower bounds in…
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Taxonomy
TopicsDistributed Sensor Networks and Detection Algorithms · Statistical Methods and Inference · Target Tracking and Data Fusion in Sensor Networks
