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

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 pn" framework, where the dimension of the covariates pn grows to infinity at a polynomial rate o(nα) 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.