Adaptive Fused LASSO in Grouped Quantile Regression

TL;DR

This paper introduces an adaptive fused group LASSO estimator for grouped quantile regression that promotes sparsity at both the group and individual variable levels, with proven convergence and oracle properties.

Contribution

It proposes a novel adaptive fused group LASSO method for quantile regression, accommodating both fixed and diverging group numbers, with theoretical guarantees.

Findings

Estimator achieves oracle properties.

Convergence rate established under classical assumptions.

Applicable to both fixed and diverging group scenarios.

Abstract

This paper considers quantile model with grouped explanatory variables. In order to have the sparsity of the parameter groups but also the sparsity between two successive groups of variables, we propose and study an adaptive fused group LASSO quantile estimator. The number of variable groups can be fixed or divergent. We find the convergence rate under classical assumptions and we show that the proposed estimator satisfies the oracle properties.