Byzantine-Robust Distributed One-Step Estimation
提出一种只需一轮迭代的鲁棒一步估计量，解决分布式M估计中部分节点出现拜占庭故障的问题，在计算复杂度不变下比一般中位数估计量渐近效率更高，还能处理中心处理器上的异常或缺失样本。
This paper proposes a Robust One-Step Estimator (ROSE) with one round of iteration to solve the Byzantine failure problem in distributed M-estimation when a moderate fraction of node machines experience Byzantine failures. The defined estimator has higher asymptotic relative efficiency than general median estimators without increasing the order of computational complexity. It can also cope with the problems involving anomalous or missing samples on the central processor. We prove the asymptotic normality when the dimension p of parameter vector diverges as the sample size goes to infinity, and under mild assumptions, derive the convergence rate. Numerical simulations and a real data application are conducted to evidence its effectiveness and robustness.