  Subsampling is an effective approach to alleviate the computational burden
associated with large-scale datasets. Nevertheless, existing subsampling
estimators incur a substantial loss in estimation efficiency compared to
estimators based on the full dataset. Specifically, the convergence rate of
existing subsampling estimators is typically $n^{-1/2}$ rather than $N^{-1/2}$,
where $n$ and $N$ denote the subsample and full data sizes, respectively. This
paper proposes a subsampled one-step (SOS) method to mitigate the estimation
efficiency loss utilizing the asymptotic expansions of the subsampling and
full-data estimators. The resulting SOS estimator is computationally efficient
and achieves a fast convergence rate of $\max\{n^{-1}, N^{-1/2}\}$ rather than
$n^{-1/2}$. We establish the asymptotic distribution of the SOS estimator,
which can be non-normal in general, and construct confidence intervals on top
of the asymptotic distribution. Furthermore, we prove that the SOS estimator is
asymptotically normal and equivalent to the full data-based estimator when $n /
\sqrt{N} \to \infty$.Simulation studies and real data analyses were conducted
to demonstrate the finite sample performance of the SOS estimator. Numerical
results suggest that the SOS estimator is almost as computationally efficient
as the uniform subsampling estimator while achieving similar estimation
efficiency to the full data-based estimator.
