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The dual and degrees of freedom of linearly constrained generalized lasso

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  • Hu, Qinqin
  • Zeng, Peng
  • Lin, Lu

Abstract

The lasso and its variants have attracted much attention recently because of its ability of simultaneous estimation and variable selection. When some prior knowledge exists in applications, the performance of estimation and variable selection can be further improved by incorporating the prior knowledge as constraints on parameters. In this article, we consider linearly constrained generalized lasso, where the constraints are either linear inequalities or equalities or both. The dual of the problem is derived, which is a much simpler problem than the original one. As a by-product, a coordinate descent algorithm is feasible to solve the dual. A formula for the number of degrees of freedom is derived. The method for selecting tuning parameter is also discussed.

Suggested Citation

  • Hu, Qinqin & Zeng, Peng & Lin, Lu, 2015. "The dual and degrees of freedom of linearly constrained generalized lasso," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 13-26.
    • Handle: RePEc:eee:csdana:v:86:y:2015:i:c:p:13-26
    DOI: 10.1016/j.csda.2014.12.010
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    References listed on IDEAS

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    Cited by:

    1. Peng Zeng & Qinqin Hu & Xiaoyu Li, 2017. "Geometry and Degrees of Freedom of Linearly Constrained Generalized Lasso," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 989-1008, December.
    2. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    3. Xu, Bin & Lin, Boqiang, 2016. "Assessing CO2 emissions in China’s iron and steel industry: A dynamic vector autoregression model," Applied Energy, Elsevier, vol. 161(C), pages 375-386.
    4. Andrew Butler & Roy H. Kwon, 2021. "Data-driven integration of norm-penalized mean-variance portfolios," Papers 2112.07016, arXiv.org, revised Nov 2022.
    5. Rafael Blanquero & Emilio Carrizosa & Pepa Ramírez-Cobo & M. Remedios Sillero-Denamiel, 2021. "A cost-sensitive constrained Lasso," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 121-158, March.
    6. Yongxin Liu & Peng Zeng & Lu Lin, 2021. "Degrees of freedom for regularized regression with Huber loss and linear constraints," Statistical Papers, Springer, vol. 62(5), pages 2383-2405, October.

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