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Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits

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  • He, Qianchuan
  • Kong, Linglong
  • Wang, Yanhua
  • Wang, Sijian
  • Chan, Timothy A.
  • Holland, Eric

Abstract

Genetic studies often involve quantitative traits. Identifying genetic features that influence quantitative traits can help to uncover the etiology of diseases. Quantile regression method considers the conditional quantiles of the response variable, and is able to characterize the underlying regression structure in a more comprehensive manner. On the other hand, genetic studies often involve high-dimensional genomic features, and the underlying regression structure may be heterogeneous in terms of both effect sizes and sparsity. To account for the potential genetic heterogeneity, including the heterogeneous sparsity, a regularized quantile regression method is introduced. The theoretical property of the proposed method is investigated, and its performance is examined through a series of simulation studies. A real dataset is analyzed to demonstrate the application of the proposed method.

Suggested Citation

  • He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:222-239
    DOI: 10.1016/j.csda.2015.10.007
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    Cited by:

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    2. Miriam Steurer & Robert Hill, 2019. "Metrics for Evaluating the Performance of Automated Valuation Models," Graz Economics Papers 2019-02, University of Graz, Department of Economics.
    3. Su, Miaomiao & Wang, Qihua, 2022. "A convex programming solution based debiased estimator for quantile with missing response and high-dimensional covariables," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    4. Zhao, Weihua & Zhou, Yan & Lian, Heng, 2018. "Time-varying quantile single-index model for multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 32-49.
    5. Xu, Bin & Lin, Boqiang, 2016. "A quantile regression analysis of China's provincial CO2 emissions: Where does the difference lie?," Energy Policy, Elsevier, vol. 98(C), pages 328-342.
    6. Wang, Yue & Zhou, Yan & Li, Rui & Lian, Heng, 2022. "Sparse high-dimensional semi-nonparametric quantile regression in a reproducing kernel Hilbert space," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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