  Distributed computing is critically important for modern statistical
analysis. Herein, we develop a distributed quasi-Newton (DQN) framework with
excellent statistical, computation, and communication efficiency. In the DQN
method, no Hessian matrix inversion or communication is needed. This
considerably reduces the computation and communication complexity of the
proposed method. Notably, related existing methods only analyze numerical
convergence and require a diverging number of iterations to converge. However,
we investigate the statistical properties of the DQN method and theoretically
demonstrate that the resulting estimator is statistically efficient over a
small number of iterations under mild conditions. Extensive numerical analyses
demonstrate the finite sample performance.
