论文标题
通用线性模型的沟通效率分布式估计器具有不同数量的协变量
Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates
论文作者
论文摘要
分布式统计推断最近引起了极大的关注。在“大$ n $，$ n $，$ n $”下的广义线性模型建立了最大似然估计器（MLE），一步MLE和总估计方程估计器的渐近效率，在polynomial rage $ o o（n $ o o o o o o o o o o o o o o o o o o o o o（$ o o o o o o o o o o o o o o o o o的$ n $ a $ $）然后提出了一种新颖的方法，以通过两轮通信获得大规模分布数据的渐近有效估计器。在这种新颖的方法中，对服务器数量的假设更加轻松，因此对于现实世界的应用而言。模拟和案例研究表明了所提出的估计量的有限样本性能令人满意。
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 $o(n^α)$ for some $0<α<1$. 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.
