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Online bootstrap inference for the geometric median

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  • Cheng, Guanghui
  • Xiong, Qiang
  • Lin, Ruitao

Abstract

In real-world applications, the geometric median is a natural quantity to consider for robust inference of location or central tendency, particularly when dealing with non-standard or irregular data distributions. An innovative online bootstrap inference algorithm, using the averaged nonlinear stochastic gradient algorithm, is proposed to make statistical inference about the geometric median from massive datasets. The method is computationally fast and memory-friendly, and it is easy to update as new data is received sequentially. The validity of the proposed online bootstrap inference is theoretically justified. Simulation studies under a variety of scenarios are conducted to demonstrate its effectiveness and efficiency in terms of computation speed and memory usage. Additionally, the online inference procedure is applied to a large publicly available dataset for skin segmentation.

Suggested Citation

  • Cheng, Guanghui & Xiong, Qiang & Lin, Ruitao, 2024. "Online bootstrap inference for the geometric median," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:csdana:v:197:y:2024:i:c:s0167947324000768
    DOI: 10.1016/j.csda.2024.107992
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    References listed on IDEAS

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    1. Axel Bücher & Ivan Kojadinovic, 2019. "A Note on Conditional Versus Joint Unconditional Weak Convergence in Bootstrap Consistency Results," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1145-1165, September.
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    4. Liu, Ruiqi & Yuan, Mingao & Shang, Zuofeng, 2022. "Online statistical inference for parameters estimation with linear-equality constraints," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    5. Godichon-Baggioni, Antoine, 2016. "Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 209-222.
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