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Optimal subsampling for quantile regression in big data

Author

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  • Haiying Wang
  • Yanyuan Ma

Abstract

SummaryWe investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the asymptotic variance-covariance matrix for a linearly transformed parameter estimator and the other minimizes that of the original parameter estimator. The former does not depend on the densities of the responses given covariates and is easy to implement. Algorithms based on optimal subsampling probabilities are proposed and asymptotic distributions, and the asymptotic optimality of the resulting estimators are established. Furthermore, we propose an iterative subsampling procedure based on the optimal subsampling probabilities in the linearly transformed parameter estimation which has great scalability to utilize available computational resources. In addition, this procedure yields standard errors for parameter estimators without estimating the densities of the responses given the covariates. We provide numerical examples based on both simulated and real data to illustrate the proposed method.

Suggested Citation

  • Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    • Handle: RePEc:oup:biomet:v:108:y:2021:i:1:p:99-112.
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    File URL: http://hdl.handle.net/10.1093/biomet/asaa043
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    Citations

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    Cited by:

    1. Daouia, Abdelaati & Padoan, Simone A. & Stupfler, Gilles, 2022. "Optimal weighted pooling for inference about the tail index and extreme quantiles," TSE Working Papers 22-1322, Toulouse School of Economics (TSE), revised 07 Jun 2023.
    2. Tianzhen Wang & Haixiang Zhang, 2022. "Optimal subsampling for multiplicative regression with massive data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 418-449, November.
    3. Deng, Jiayi & Huang, Danyang & Ding, Yi & Zhu, Yingqiu & Jing, Bingyi & Zhang, Bo, 2024. "Subsampling spectral clustering for stochastic block models in large-scale networks," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    4. Xiaohui Yuan & Yong Li & Xiaogang Dong & Tianqing Liu, 2022. "Optimal subsampling for composite quantile regression in big data," Statistical Papers, Springer, vol. 63(5), pages 1649-1676, October.
    5. Peng, Cheng & Kouri, Drew P. & Uryasev, Stan, 2024. "Efficient and robust optimal design for quantile regression based on linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    6. Seong‐H. Lee & Yanyuan Ma & Ying Wei & Jinbo Chen, 2023. "Optimal sampling for positive only electronic health record data," Biometrics, The International Biometric Society, vol. 79(4), pages 2974-2986, December.
    7. Jiadi Yang & Jinjin Wang, 2022. "TV program innovation and teaching under big data background in all media era," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1031-1041, December.
    8. 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.
    9. Ziyang Wang & HaiYing Wang & Nalini Ravishanker, 2023. "Subsampling in Longitudinal Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    10. Jun Yu & Jiaqi Liu & HaiYing Wang, 2023. "Information-based optimal subdata selection for non-linear models," Statistical Papers, Springer, vol. 64(4), pages 1069-1093, August.

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