# Statistical Mean Estimation with Coded Relayed Observations

arXiv: https://arxiv.org/abs/2505.09098 · HTML: https://mlsanity.com/paper/2505.09098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 14 May 2025.

## Builds on (most cited first, 6 of 6)

- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [Interactive Inference under Information Constraints](https://mlsanity.com/paper/2007.10976/) (2020)
- [On the optimality of coin-betting for mean estimation](https://mlsanity.com/paper/2412.02640/) (2024)
- [Teaching and learning in uncertainty](https://mlsanity.com/paper/1901.07063/) (2019)
- [The Information Velocity of Packet-Erasure Links](https://mlsanity.com/paper/2201.04257/) (2022)

## Abstract (arXiv)

We consider a problem of statistical mean estimation in which the samples are not observed directly, but are instead observed by a relay (``teacher'') that transmits information through a memoryless channel to the decoder (``student''), who then produces the final estimate. We consider the minimax estimation error in the large deviations regime, and establish achievable error exponents that are tight in broad regimes of the estimation accuracy and channel quality. In contrast, two natural baseline methods are shown to yield strictly suboptimal error exponents. We initially focus on Bernoulli sources and binary symmetric channels, and then generalize to sub-Gaussian and heavy-tailed settings along with arbitrary discrete memoryless channels.