Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates

• URL: http://arxiv.org/abs/2001.06194v2
• Date: Thu, 13 Aug 2020 17:25:05 GMT
• Title: Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates
• Authors: Ping Zhou, Zhen Yu, Jingyi Ma, Maozai Tian, and Ye Fan
• Abstract summary: A novel method is proposed to obtain anally 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.
• Score: 7.427903819459701
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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