  This paper proposes a moment-assisted subsampling method which can improve
the estimation efficiency of existing subsampling estimators. The motivation
behind this approach stems from the fact that sample moments can be efficiently
computed even if the sample size of the whole data set is huge. Through the
generalized method of moments, this method incorporates informative sample
moments of the whole data into the subsampling estimator. The moment-assisted
estimator is asymptotically normal and has a smaller asymptotic variance
compared to the corresponding estimator without incorporating sample moments of
the whole data. The asymptotic variance of the moment-assisted estimator
depends on the specific sample moments incorporated. Under the uniform
subsampling probability, we derive the optimal moment that minimizes the
resulting asymptotic variance in terms of Loewner order. Moreover, the
moment-assisted subsampling estimator can be rapidly computed through one-step
linear approximation. Simulation studies and a real data analysis were
conducted to compare the proposed method with existing subsampling methods.
Numerical results show that the moment-assisted subsampling method performs
competitively across different settings. This suggests that incorporating the
sample moments of the whole data can enhance existing subsampling technique.

Methodology