2019/11/04 by Álvaro Méndez Civieta, Civieta, Álvaro Méndez, M. Carmen Aguilera‐Morillo +3
Engineering · Mathematics · #Advanced Statistical Methods and Models #Applications (stat.AP) #Control Systems and Identification #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1911.01081
openalex publication_date 2019/11/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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 √(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.