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Regularized partially functional quantile regression

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  • Yao, Fang
  • Sue-Chee, Shivon
  • Wang, Fan

Abstract

We propose a regularized partially functional quantile regression model where the response variable is scalar while the explanatory variables involve both infinite-dimensional predictor processes viewed as functional data, and high-dimensional scalar covariates. Despite extensive work focusing on functional linear models, little effort has been devoted to the development of robust methodologies that tackle the scenarios of non-normal errors. This motivates our proposal of functional quantile regression that seeks an alternative and robust solution to least squares type procedures within the partially functional regression framework. We focus on estimating and selecting the important variables in the high-dimensional covariates, which is complicated by the infinite-dimensional functional predictor. We establish the asymptotic properties of the resulting shrinkage estimator, and empirical illustrations are given by simulation and an application to a brain imaging dataset.

Suggested Citation

  • Yao, Fang & Sue-Chee, Shivon & Wang, Fan, 2017. "Regularized partially functional quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 39-56.
    • Handle: RePEc:eee:jmvana:v:156:y:2017:i:c:p:39-56
    DOI: 10.1016/j.jmva.2017.02.001
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    Cited by:

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    2. Yu, Dengdeng & Zhang, Li & Mizera, Ivan & Jiang, Bei & Kong, Linglong, 2019. "Sparse wavelet estimation in quantile regression with multiple functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 12-29.
    3. Yanping Hu & Zhongqi Pang, 2023. "Partially Functional Linear Models with Linear Process Errors," Mathematics, MDPI, vol. 11(16), pages 1-18, August.
    4. Tang Qingguo & Bian Minjie, 2021. "Estimation for functional linear semiparametric model," Statistical Papers, Springer, vol. 62(6), pages 2799-2823, December.
    5. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    6. 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.
    7. 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.
    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. Jianing Fan & Hans‐Georg Müller, 2022. "Conditional distribution regression for functional responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 502-524, June.
    10. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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