Adaptive group LASSO selection in quantile models

TL;DR

This paper introduces an adaptive group LASSO quantile estimator for linear models with grouped variables, effective even with outliers or non-zero mean errors, and demonstrates its theoretical properties and practical performance.

Contribution

It develops a novel adaptive group LASSO method for quantile regression, establishing its sparsity and asymptotic normality under various scenarios.

Findings

Estimator achieves sparsity and normality properties.

Monte Carlo simulations confirm theoretical results.

Method performs well with outliers and non-zero mean errors.

Abstract

The paper considers a linear model with grouped explanatory variables. If the model errors are not with zero mean and bounded variance or if model contains outliers, then the least squares framework is not appropriate. Thus, the quantile regression is an interesting alternative. In order to automatically select the relevant variable groups, we propose and study here the adaptive group LASSO quantile estimator. We establish the sparsity and asymptotic normality of the proposed estimator in two cases: fixed number and divergent number of variable groups. Numerical study by Monte Carlo simulations confirms the theoretical results and illustrates the performance of the proposed estimator.