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Quantile regression for functional partially linear model in ultra-high dimensions

Author

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  • Ma, Haiqiang
  • Li, Ting
  • Zhu, Hongtu
  • Zhu, Zhongyi

Abstract

Quantile regression for functional partially linear model in ultra-high dimensions is proposed and studied. By focusing on the conditional quantiles, where conditioning is on both multiple random processes and high-dimensional scalar covariates, the proposed model can lead to a comprehensive description of the scalar response. To select and estimate important variables, a double penalized functional quantile objective function with two nonconvex penalties is developed, and the optimal tuning parameters involved can be chosen by a two-step technique. Based on the difference convex analysis (DCA), the asymptotic properties of the resulting estimators are established, and the convergence rate of the prediction of the conditional quantile function can be obtained. Simulation studies demonstrate a competitive performance against the existing approach. A real application to Alzheimer’s Disease Neuroimaging Initiative (ADNI) data is used to illustrate the practicality of the proposed model.

Suggested Citation

  • Ma, Haiqiang & Li, Ting & Zhu, Hongtu & Zhu, Zhongyi, 2019. "Quantile regression for functional partially linear model in ultra-high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 135-147.
    • Handle: RePEc:eee:csdana:v:129:y:2019:i:c:p:135-147
    DOI: 10.1016/j.csda.2018.06.005
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    References listed on IDEAS

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    4. Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
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    Citations

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    Cited by:

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    3. Chengxin Wu & Nengxiang Ling, 2025. "Partially functional linear expectile regression model with missing observations," Computational Statistics, Springer, vol. 40(7), pages 3981-4005, September.
    4. Ufuk Beyaztas & Han Lin Shang & Aylin Alin, 2022. "Function-on-Function Partial Quantile Regression," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 149-174, March.
    5. Yanxia Liu & Zhihao Wang & Maozai Tian & Keming Yu, 2024. "Estimation and variable selection for generalized functional partially varying coefficient hybrid models," Statistical Papers, Springer, vol. 65(1), pages 93-119, February.
    6. Ufuk Beyaztas & Han Lin Shang & Semanur Saricam, 2025. "Penalized function-on-function linear quantile regression," Computational Statistics, Springer, vol. 40(1), pages 301-329, January.
    7. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    8. Liang, Weijuan & Zhang, Qingzhao & Ma, Shuangge, 2023. "Locally sparse quantile estimation for a partially functional interaction model," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    9. Zhiqiang Jiang & Zhensheng Huang & Jing Zhang, 2023. "Functional single-index composite quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 595-603, July.
    10. Chengxin Wu & Nengxiang Ling & Philippe Vieu & Guoliang Fan, 2025. "Composite quantile estimation in partially functional linear regression model with randomly censored responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 28-47, March.
    11. Sanying Feng & Menghan Zhang & Tiejun Tong, 2022. "Variable selection for functional linear models with strong heredity constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 321-339, April.

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