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Bagging is a useful method for large-scale statistical analysis, especially
when the computing resources are very limited. We study here the asymptotic
properties of bagging estimators for $M$-estimation problems but with massive
datasets. We theoretically prove that the resulting estimator is consistent and
asymptotically normal under appropriate conditions. The results show that the
bagging estimator can achieve the optimal statistical efficiency, provided that
the bagging subsample size and the number of subsamples are sufficiently large.
Moreover, we derive a variance estimator for valid asymptotic inference. All
theoretical findings are further verified by extensive simulation studies.
Finally, we apply the bagging method to the US Airline Dataset to demonstrate
its practical usefulness.
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