Expected shortfall (ES) is widely used for characterizing the tail of a distribution across various fields, particularly in financial risk management. In this paper, we explore a two-step procedure that leverages an orthogonality property to reduce sensitivity to nuisance parameters when estimating within a joint quantile and expected shortfall regression framework. For high-dimensional sparse models, we propose a robust $\ell_1$-penalized two-step approach capable of handling heavy-tailed data distributions. We establish non-asymptotic estimation error bounds and propose an appropriate growth rate for the diverging robustification parameter. To facilitate statistical inference for certain linear combinations of the ES regression coefficients, we construct debiased estimators and develop their asymptotic distributions, which form the basis for constructing valid confidence intervals. We validate the proposed method through simulation studies, demonstrating its effectiveness in high-dimensional linear models with heavy-tailed errors.

Random forests are powerful non-parametric regression method but are severely limited in their usage in the presence of randomly censored observations, and naively applied can exhibit poor predictive performance due to the incurred biases. Based on a local adaptive representation of random forests, we develop its regression adjustment for randomly censored regression quantile models. Regression adjustment is based on a new estimating equation that adapts to censoring and leads to quantile score whenever the data do not exhibit censoring. The proposed procedure named censored quantile regression forest, allows us to estimate quantiles of time-to-event without any parametric modeling assumption. We establish its consistency under mild model specifications. Numerical studies showcase a clear advantage of the proposed procedure.