  This article introduces subbagging (subsample aggregating) estimation
approaches for big data analysis with memory constraints of computers.
Specifically, for the whole dataset with size $N$, $m_N$ subsamples are
randomly drawn, and each subsample with a subsample size $k_N\ll N$ to meet the
memory constraint is sampled uniformly without replacement. Aggregating the
estimators of $m_N$ subsamples can lead to subbagging estimation. To analyze
the theoretical properties of the subbagging estimator, we adapt the incomplete
$U$-statistics theory with an infinite order kernel to allow overlapping drawn
subsamples in the sampling procedure. Utilizing this novel theoretical
framework, we demonstrate that via a proper hyperparameter selection of $k_N$
and $m_N$, the subbagging estimator can achieve $\sqrt{N}$-consistency and
asymptotic normality under the condition $(k_Nm_N)/N\to \alpha \in (0,\infty]$.
Compared to the full sample estimator, we theoretically show that the
$\sqrt{N}$-consistent subbagging estimator has an inflation rate of $1/\alpha$
in its asymptotic variance. Simulation experiments are presented to demonstrate
the finite sample performances. An American airline dataset is analyzed to
illustrate that the subbagging estimate is numerically close to the full sample
estimate, and can be computationally fast under the memory constraint.
