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Robust optimal subsampling based on weighted asymmetric least squares

Author

Listed:
  • Min Ren

    (Qufu Normal University)

  • Shengli Zhao

    (Qufu Normal University)

  • Mingqiu Wang

    (Qufu Normal University)

  • Xinbei Zhu

    (Virginia Tech University)

Abstract

With the development of contemporary science, a large amount of generated data includes heterogeneity and outliers in the response and/or covariates. Furthermore, subsampling is an effective method to overcome the limitation of computational resources. However, when data include heterogeneity and outliers, incorrect subsampling probabilities may select inferior subdata, and statistic inference on this subdata may have a far inferior performance. Combining the asymmetric least squares and $$L_2$$ L 2 estimation, this paper proposes a double-robustness framework (DRF), which can simultaneously tackle the heterogeneity and outliers in the response and/or covariates. The Poisson subsampling is implemented based on the DRF for massive data, and a more robust probability will be derived to select the subdata. Under some regularity conditions, we establish the asymptotic properties of the subsampling estimator based on the DRF. Numerical studies and actual data demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Min Ren & Shengli Zhao & Mingqiu Wang & Xinbei Zhu, 2024. "Robust optimal subsampling based on weighted asymmetric least squares," Statistical Papers, Springer, vol. 65(4), pages 2221-2251, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01480-7
    DOI: 10.1007/s00362-023-01480-7
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    References listed on IDEAS

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