  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.
