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

TL;DR

This paper introduces a communication-efficient distributed estimation method for generalized linear models with a diverging number of covariates, achieving asymptotic efficiency with minimal communication rounds.

Contribution

It proposes a novel two-round communication method for distributed generalized linear models that relaxes server number assumptions and maintains asymptotic efficiency.

Findings

Method achieves asymptotic efficiency in high-dimensional settings.

Simulation results confirm good finite-sample performance.

Case study demonstrates practical applicability.

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.