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A Subsampled Double Bootstrap for Massive Data

Author

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  • Srijan Sengupta
  • Stanislav Volgushev
  • Xiaofeng Shao

Abstract

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little sacrifice of statistical accuracy. Building on BLB and the idea of fast double bootstrap, we propose a new resampling method, the subsampled double bootstrap, for both independent data and time series data. We establish consistency of the subsampled double bootstrap under mild conditions for both independent and dependent cases. Methodologically, the subsampled double bootstrap is superior to BLB in terms of running time, more sample coverage, and automatic implementation with less tuning parameters for a given time budget. Its advantage relative to BLB and bootstrap is also demonstrated in numerical simulations and a data illustration. Supplementary materials for this article are available online.

Suggested Citation

  • Srijan Sengupta & Stanislav Volgushev & Xiaofeng Shao, 2016. "A Subsampled Double Bootstrap for Massive Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1222-1232, July.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:515:p:1222-1232
    DOI: 10.1080/01621459.2015.1080709
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    Cited by:

    1. Guangbao Guo & Yue Sun & Xuejun Jiang, 2020. "A partitioned quasi-likelihood for distributed statistical inference," Computational Statistics, Springer, vol. 35(4), pages 1577-1596, December.
    2. Dimitris N Politis, 2024. "Scalable subsampling: computation, aggregation and inference," Biometrika, Biometrika Trust, vol. 111(1), pages 347-354.
    3. Xuejun Ma & Shaochen Wang & Wang Zhou, 2022. "Statistical inference in massive datasets by empirical likelihood," Computational Statistics, Springer, vol. 37(3), pages 1143-1164, July.
    4. Kaizhao Liu & Jose Blanchet & Lexing Ying & Yiping Lu, 2024. "Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty," Papers 2404.19145, arXiv.org, revised Apr 2024.
    5. Ma, Xuejun & Wang, Shaochen & Zhou, Wang, 2021. "Testing multivariate quantile by empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 182(C).

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