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Quantile regression : a penalization approach

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  • Méndez Civieta, Álvaro
  • Aguilera Morillo, María del Carmen
  • Lillo Rodríguez, Rosa Elvira

Abstract

Sparse group LASSO (SGL) is a penalization technique used in regression problems where the covariates have a natural grouped structure and provides solutions that are both between and within group sparse. In this paper the SGL is introduced to the quantile regression (QR) framework, and a more flexible version, the adaptive sparse group LASSO (ASGL), is proposed. This proposal adds weights to the penalization improving prediction accuracy. Usually, adaptive weights are taken as a function of the original non-penalized solution model. This approach is only feasible in the n > p framework. In this work, a solution that allows using adaptive weights in high-dimensional scenarios is proposed. The benefits of this proposal are studied both in synthetic and real datasets.

Suggested Citation

  • Méndez Civieta, Álvaro & Aguilera Morillo, María del Carmen & Lillo Rodríguez, Rosa Elvira, 2019. "Quantile regression : a penalization approach," DES - Working Papers. Statistics and Econometrics. WS 28428, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:28428
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    Quantile Regression;

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