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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关于具有海量数据集的 bagging 估计器的渐近性质

Bagging 是一种用于大规模统计分析的有用方法，尤其是在计算资源非常有限的情况下。我们在这里研究装袋估计量的渐近性质$米$- 估计问题，但具有大量数据集。我们从理论上证明，在适当的条件下，所得估计量是一致的且渐近正态的。结果表明，如果 bagging 子样本大小和子样本数量足够大，bagging 估计器可以达到最优的统计效率。此外，我们推导出有效渐近推理的方差估计量。所有理论发现都通过广泛的模拟研究得到进一步验证。最后，我们将 bagging 方法应用于美国航空公司数据集，以证明其实用性。