2021/02/28 by Tao Zou, Xian Li, Zou, Tao +5
Mathematics · #Advanced Statistical Methods and Models #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #Fuzzy Systems and Optimization #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2103.00631
openalex publication_date 2021/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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, mN subsamples are randomly drawn, and each subsample with a subsample size kN≪ N to meet the memory constraint is sampled uniformly without replacement. Aggregating the estimators of mN 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 kN and mN, the subbagging estimator can achieve √(N)-consistency and asymptotic normality under the condition (kNmN)/N→ α∈ (0,∞]. Compared to the full sample estimator, we theoretically show that the √(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.