ADAPTIVE ROBUST VARIABLE SELECTION.

ABSTRACT: Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L₁-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L₁-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is e

SUBMITTER: Fan J 

PROVIDER: S-EPMC4286898 | biostudies-literature | 2014 Feb

REPOSITORIES: biostudies-literature