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Distributed inference for two‐sample U‐statistics in massive data analysis

Author

Listed:
  • Bingyao Huang
  • Yanyan Liu
  • Liuhua Peng

Abstract

This paper considers distributed inference for two‐sample U‐statistics under the massive data setting. In order to reduce the computational complexity, this paper proposes distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics. The blockwise linear two‐sample U‐statistic, which requires less communication cost, is more computationally efficient especially when the data are stored in different locations. The asymptotic properties of both types of distributed two‐sample U‐statistics are established. In addition, this paper proposes bootstrap algorithms to approximate the distributions of distributed two‐sample U‐statistics and blockwise linear two‐sample U‐statistics for both nondegenerate and degenerate cases. The distributed weighted bootstrap for the distributed two‐sample U‐statistic is new in the literature. The proposed bootstrap procedures are computationally efficient and are suitable for distributed computing platforms with theoretical guarantees. Extensive numerical studies illustrate that the proposed distributed approaches are feasible and effective.

Suggested Citation

  • Bingyao Huang & Yanyan Liu & Liuhua Peng, 2023. "Distributed inference for two‐sample U‐statistics in massive data analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1090-1115, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1090-1115
    DOI: 10.1111/sjos.12620
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    References listed on IDEAS

    as
    1. 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.
    2. Ariel Kleiner & Ameet Talwalkar & Purnamrita Sarkar & Michael I. Jordan, 2014. "A scalable bootstrap for massive data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 795-816, September.
    3. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
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