Adaptive sparse group LASSO in quantile regression

Alvaro Mendez-Civieta (), M. Carmen Aguilera-Morillo and Rosa E. Lillo
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Alvaro Mendez-Civieta: University Carlos III of Madrid
M. Carmen Aguilera-Morillo: uc3m-Santander Big Data Institute
Rosa E. Lillo: University Carlos III of Madrid

Advances in Data Analysis and Classification, 2021, vol. 15, issue 3, No 2, 547-573

Abstract: 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.

Keywords: High-dimension; Penalization; Regularization; Prediction; Weight calculation; 62J07 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11634-020-00413-8

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