Distributed Gaussian Mean Estimation under Communication Constraints: Optimal Rates and Communication-efficient Algorithms
Tony Cai and Hongji Wei
Although optimal estimation of a Gaussian mean is relatively simple in the conventional setting, it is quite involved under communication constraints, both in terms of the optimal procedure design and the lower bound argument. An essential step is the decomposition of the minimax estimation problem into two stages, localization and refinement. This critical decomposition provides a framework for both the lower bound analysis and optimal procedure design. The optimality results and techniques developed in the present paper can be useful for solving other problems such as distributed nonparametric function estimation and sparse signal recovery.