Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for generalized linear models under the "large $n$, diverging $p_n$" framework, where the dimension of the covariates $p_n$ grows to infinity at a polynomial rate $o(n^\alpha)$ for some $0<\alpha<1$. Then a novel method is proposed to obtain an asymptotically efficient estimator for large-scale distributed data by two rounds of communication. In this novel method, the assumption on the number of servers is more relaxed and thus practical for real-world applications. Simulations and a case study demonstrate the satisfactory finite-sample performance of the proposed estimators.

中文翻译：

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具有发散数量协变量的广义线性模型的通信高效分布式估计器

分布式统计推断最近引起了极大的关注。在“大$n$，发散$p_n$”框架下，建立了广义线性模型的最大似然估计器（MLE）、一步MLE和聚合估计方程估计器的渐近效率，其中对于某些 $0<\alpha<1$，协变量 $p_n$ 以多项式速率 $o(n^\alpha)$ 增长到无穷大。然后提出了一种新方法，通过两轮通信获得大规模分布式数据的渐近有效估计量。在这种新颖的方法中，对服务器数量的假设更加宽松，因此适用于实际应用程序。模拟和案例研究证明了所提出的估计器的令人满意的有限样本性能。