Comput. Stat. Data Anal. | 2021
Communication-Efficient Distributed Estimator for Generalized Linear Models with a Diverging Number of Covariates
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.