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Optimal subsampling for composite quantile regression model in massive data

Author

Listed:
  • Yujing Shao

    (Nankai University)

  • Lei Wang

    (Nankai University)

Abstract

The composite quantile regression (CQR) estimator is a robust and efficient alternative to the ordinary least squares estimator and single quantile regression estimator in linear models. For massive data, two different optimal subsampling probabilities through minimizing the trace of the asymptotic variance–covariance matrix for a linearly transformed parameter estimator and the asymptotic mean squared error of the resultant estimator are proposed to downsize the data volume and reduce the computational burden. Furthermore, to improve the efficiency of the ordinary CQR, the optimal subsampling for the weighted CQR estimator is also studied. We also propose iterative subsampling procedures based on two optimal subsampling probabilities to estimate the variance–covariance matrix. The finite-sample performance of the proposed estimators is studied through simulations and an application to household electric power consumption data is also presented.

Suggested Citation

  • Yujing Shao & Lei Wang, 2022. "Optimal subsampling for composite quantile regression model in massive data," Statistical Papers, Springer, vol. 63(4), pages 1139-1161, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01271-y
    DOI: 10.1007/s00362-021-01271-y
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    References listed on IDEAS

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    1. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
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    3. Jiang, Xuejun & Li, Jingzhi & Xia, Tian & Yan, Wanfeng, 2016. "Robust and efficient estimation with weighted composite quantile regression," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 413-423.
    4. Jiang, Rong & Qian, Wei-Min & Zhou, Zhan-Gong, 2016. "Weighted composite quantile regression for single-index models," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 34-48.
    5. Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    6. HaiYing Wang & Rong Zhu & Ping Ma, 2018. "Optimal Subsampling for Large Sample Logistic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 829-844, April.
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