Huber tuning-parameter selection under model misspecification

Determine how to select the Huber tuning parameter theoretically under model misspecification when the squared loss in the two-stage Expected Shortfall Model Averaging framework is replaced by the Huber loss.

Background

The paper notes that robustness to sub-Gaussian or heavy-tailed data can be pursued by replacing the second-stage squared loss in the two-stage Expected Shortfall Model Averaging framework with an adaptive Huber loss. Although this substitution is computationally feasible, selecting the Huber tuning parameter under model misspecification presents unresolved theoretical difficulties. The authors explicitly defer this issue to future research.