A0975
Title: High-dimensional robust inference via the debiased rank lasso
Authors: Yoshimasa Uematsu - Hitotsubashi University (Japan) [presenting]
Kazuma Sawaya - The University of Tokyo (Japan)
Abstract: An inferential framework robust to heavy-tailed error distributions in high-dimensional linear regression models is proposed. A key ingredient of the robustness is the rank lasso, but the estimator is not asymptotically normally distributed thanks to the regularization. We propose the debiased rank lasso estimator, which can establish the asymptotic normality. Furthermore, using this estimator, we develop a method for the robust simultaneous inference that can discover important variables in the linear regression models with the false discovery rate (FDR) controlled under the preassigned level. We also confirm the performance through extensive numerical simulations. We find that our procedure controls the FDR and exhibits higher power than the original method when the error distribution is heavy-tailed.
