  High-dimensional penalized rank regression is a powerful tool for modeling
high-dimensional data due to its robustness and estimation efficiency. However,
the non-smoothness of the rank loss brings great challenges to the computation.
To solve this critical issue, high-dimensional convoluted rank regression is
recently proposed, and penalized convoluted rank regression estimators are
introduced. However, these developed estimators cannot be directly used to make
inference. In this paper, we investigate the inference problem of
high-dimensional convoluted rank regression. We first establish estimation
error bounds of penalized convoluted rank regression estimators under weaker
conditions on the predictors. Based on the penalized convoluted rank regression
estimators, we further introduce a debiased estimator. We then provide Bahadur
representation for our proposed estimator. We further develop simultaneous
inference procedures. A novel bootstrap procedure is proposed and its
theoretical validity is also established. Finally, simulation and real data
analysis are conducted to illustrate the merits of our proposed methods.
