On the Subbagging Estimation for Massive Data
This provides a scalable solution for big data analysis in statistics and machine learning, though it is incremental as it builds on existing subsampling and aggregation techniques.
The paper tackles the problem of statistical estimation with massive datasets under memory constraints by proposing a subbagging (subsample aggregating) method, achieving √N-consistency and asymptotic normality with an inflation rate of 1/α in asymptotic variance compared to full-sample estimators.
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 $(k_Nm_N)/N\to α\in (0,\infty]$. Compared to the full sample estimator, we theoretically show that the $\sqrt{N}$-consistent subbagging estimator has an inflation rate of $1/α$ 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.