Distributed adaptive Gaussian mean estimation with unknown variance: Interactive protocol helps adaptation
The Annals of Statistics · 2022 · Volume 50 · Issue 4
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.
Keywords
62B10, 62F12, 62F30, adaptive estimation, communication constraints, Distributed learning, Gaussian mean, minimax lower bound, Optimal rate of convergence
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