A Distributed One-Step Estimator
This work addresses the challenge of efficient large-scale statistical inference in distributed settings with limited communication bandwidth, offering an incremental improvement over existing averaging methods.
The paper tackles the problem of distributed statistical inference by proposing a one-step estimator that enhances simple averaging, achieving the same asymptotic properties as a centralized estimator with only one additional communication round. Numerical results show it significantly outperforms simple averaging in mean squared error.
Distributed statistical inference has recently attracted enormous attention. Many existing work focuses on the averaging estimator. We propose a one-step approach to enhance a simple-averaging based distributed estimator. We derive the corresponding asymptotic properties of the newly proposed estimator. We find that the proposed one-step estimator enjoys the same asymptotic properties as the centralized estimator. The proposed one-step approach merely requires one additional round of communication in relative to the averaging estimator; so the extra communication burden is insignificant. In finite sample cases, numerical examples show that the proposed estimator outperforms the simple averaging estimator with a large margin in terms of the mean squared errors. A potential application of the one-step approach is that one can use multiple machines to speed up large scale statistical inference with little compromise in the quality of estimators. The proposed method becomes more valuable when data can only be available at distributed machines with limited communication bandwidth.