Probabilistic Error Upper Bounds For Distributed Statistical Estimation

The size of modern datasets has spurred interest in distributed statistical estimation. We consider a scenario in which randomly drawn data is spread across a set of machines, and the task is to provide an estimate for the location parameter from which the data was drawn. We provide a one-shot protocol for computing this estimate which generalizes results from Braverman et al. [2], which provides a protocol under the assumption that the distribution is Gaussian, as well as from Duchi et al. [4], which assumes that the distribution is supported on the compact set [−1,1]. Like that of Braverman et al., our protocol is optimal in the case that the distribution is Gaussian