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Adaptive sparse group LASSO in quantile regression

Author

Listed:
  • Alvaro Mendez-Civieta

    (University Carlos III of Madrid
    uc3m-Santander Big Data Institute)

  • M. Carmen Aguilera-Morillo

    (uc3m-Santander Big Data Institute
    Universitat Politecnica de Valencia)

  • Rosa E. Lillo

    (University Carlos III of Madrid
    uc3m-Santander Big Data Institute)

Abstract

This paper studies the introduction of sparse group LASSO (SGL) to the quantile regression framework. Additionally, a more flexible version, an adaptive SGL is proposed based on the adaptive idea, this is, the usage of adaptive weights in the penalization. Adaptive estimators are usually focused on the study of the oracle property under asymptotic and double asymptotic frameworks. A key step on the demonstration of this property is to consider adaptive weights based on a initial $$\sqrt{n}$$ n -consistent estimator. In practice this implies the usage of a non penalized estimator that limits the adaptive solutions to low dimensional scenarios. In this work, several solutions, based on dimension reduction techniques PCA and PLS, are studied for the calculation of these weights in high dimensional frameworks. The benefits of this proposal are studied both in synthetic and real datasets.

Suggested Citation

  • Alvaro Mendez-Civieta & M. Carmen Aguilera-Morillo & Rosa E. Lillo, 2021. "Adaptive sparse group LASSO in quantile regression," 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(3), pages 547-573, September.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00413-8
    DOI: 10.1007/s11634-020-00413-8
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    References listed on IDEAS

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