College of Liberal Arts
Most of the existing high-dimensional regression procedures are sensitive to the presence of heavy-tailed errors. Some robust alternative have been proposed and their implementation relies on tuning parameters, whose optimal choices often depend on unknown noise variances. The estimate of noise variance itself is a difficult problem in high dimensions for heavy-tailed data. These researchers consider penalized Wilcoxon rank regression, which possesses a number of desirable advantages in the ultra-high dimensional scenario.