Adaptive fused LASSO in grouped quantile regression

ABSTRACT

This article considers the 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.

KEYWORDS:

• Group selection
• quantile regression
• adaptive fused LASSO
• selection consistency
• oracle properties

AMS subject classification:

• Primary 62F35
• secondary 62F12