Abstract
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.
Funding Statement
The research was supported in part by NSF Grant DMS-2015259 and NIH grants R01-GM129781 and R01-GM123056.
Citation
T. Tony Cai. Hongji Wei. "Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocol helps adaptation." Ann. Statist. 50 (4) 1992 - 2020, August 2022. https://doi.org/10.1214/21-AOS2167
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