通过中继编码传输样本，实现更优的统计均值估计。
Statistical Mean Estimation with Coded Relayed Observations
- 用中继编码方式传递样本信息，提升估计精度。
- 在大偏离率下，误差指数逼近理论最优。
- 适用于各类分布和信道，适合通信受限场景。
我们研究一种统计均值估计问题：样本不直接观测，而是由中继（教师）通过无记忆信道传给解码器（学生），由后者生成最终估计。研究大偏离率下的极小化最大估计误差，推导出在广泛精度与信道质量条件下可达的误差指数，并证明其紧致性。相比之下，两种自然基线方法的误差指数严格次优。初始分析针对伯努利源与二元对称信道，随后推广至亚高斯和重尾分布，以及任意离散无记忆信道。
原文摘要 · Abstract (English)
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.
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