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.

翻译：分布式计算对现代统计分析至关重要。本文开发了一个具有优异统计、计算和通信效率的分布式拟牛顿（DQN）框架。在DQN方法中，无需海森矩阵求逆或通信，这大大降低了所提方法的计算和通信复杂度。值得注意的是，现有相关方法仅分析数值收敛性，且需要不断增加的迭代次数才能收敛。然而，我们研究了DQN方法的统计性质，并从理论上证明，在温和条件下，所得估计量在少量迭代次数下具有统计有效性。广泛的数值分析验证了其有限样本性能。