IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v50y2023i3p1090-1115.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12620
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12620?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Xingcai Zhou & Zhaoyang Jing & Chao Huang, 2024. "Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression," Mathematics, MDPI, vol. 12(5), pages 1-53, February.
    3. Dimitris N Politis, 2024. "Scalable subsampling: computation, aggregation and inference," Biometrika, Biometrika Trust, vol. 111(1), pages 347-354.
    4. Wang, Xiaoqian & Kang, Yanfei & Hyndman, Rob J. & Li, Feng, 2023. "Distributed ARIMA models for ultra-long time series," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1163-1184.
    5. Baolin Chen & Shanshan Song & Yong Zhou, 2024. "Estimation and testing of expectile regression with efficient subsampling for massive data," Statistical Papers, Springer, vol. 65(9), pages 5593-5613, December.
    6. 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.
    7. Changgee Chang & Zhiqi Bu & Qi Long, 2023. "CEDAR: communication efficient distributed analysis for regressions," Biometrics, The International Biometric Society, vol. 79(3), pages 2357-2369, September.
    8. Ma, Xuejun & Wang, Shaochen & Zhou, Wang, 2021. "Testing multivariate quantile by empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    9. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    10. Xiang, Pengcheng & Zhou, Ling & Tang, Lu, 2024. "Transfer learning via random forests: A one-shot federated approach," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    11. Feifei Wang & Danyang Huang & Tianchen Gao & Shuyuan Wu & Hansheng Wang, 2022. "Sequential one‐step estimator by sub‐sampling for customer churn analysis with massive data sets," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1753-1786, November.
    12. Guangbao Guo & Guoqi Qian & Lu Lin & Wei Shao, 2021. "Parallel inference for big data with the group Bayesian method," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 225-243, February.
    13. Dean Eckles & Maurits Kaptein, 2019. "Bootstrap Thompson Sampling and Sequential Decision Problems in the Behavioral Sciences," SAGE Open, , vol. 9(2), pages 21582440198, June.
    14. Ren, Yimeng & Li, Zhe & Zhu, Xuening & Gao, Yuan & Wang, Hansheng, 2024. "Distributed estimation and inference for spatial autoregression model with large scale networks," Journal of Econometrics, Elsevier, vol. 238(2).
    15. Badruddoza, Syed & Amin, Modhurima & McCluskey, Jill, 2019. "Assessing the Importance of an Attribute in a Demand SystemStructural Model versus Machine Learning," Working Papers 2019-5, School of Economic Sciences, Washington State University.
    16. Yaohong Yang & Lei Wang, 2023. "Communication-efficient sparse composite quantile regression for distributed data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 261-283, April.
    17. Olhede, Sofia C. & Wolfe, Patrick J., 2018. "The future of statistics and data science," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 46-50.
    18. Wang, Kangning & Li, Shaomin, 2021. "Robust distributed modal regression for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    19. Shi, Chengchun & Lu, Wenbin & Song, Rui, 2018. "A massive data framework for M-estimators with cubic-rate," LSE Research Online Documents on Economics 102111, London School of Economics and Political Science, LSE Library.
    20. Xingcai Zhou & Yu Xiang, 2022. "ADMM-Based Differential Privacy Learning for Penalized Quantile Regression on Distributed Functional Data," Mathematics, MDPI, vol. 10(16), pages 1-28, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1090-1115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.