DISTRIBUTED ADAPTIVE GAUSSIAN MEAN ESTIMATION WITH UNKNOWN VARIANCE: INTERACTIVE PROTOCOL HELPS ADAPTATION
成果类型：
Article
署名作者：
Cai, T. Tony; Wei, Hongji
署名单位：
University of Pennsylvania
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/21-AOS2167
发表日期：
2022
页码：
1992-2020
关键词：
摘要：
Distributed estimation of a Gaussian mean with unknown variance under communication constraints is studied. Necessary and sufficient communication costs under different types of distributed protocols are derived for any estimator that is adaptively rate-optimal over a range of possible values for the variance. Communication-efficient and statistically optimal procedures are developed. The analysis reveals an interesting and important distinction among different types of distributed protocols: compared to the independent protocols, interactive protocols such as the sequential and blackboard protocols require less communication costs for rate-optimal adaptive Gaussian mean estimation. The lower bound techniques developed in the present paper are novel and can be of independent interest.