  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.
