Nonparametric estimation of expected shortfall via Bahadur-type representation and Berry–Esséen bounds

The expected shortfall is an important risk measure in financial risk management. In this paper, we study the Bahadur-type representation of an improved nonparametric expected shortfall estimator for φ-mixing financial losses without any restrictions on the mixing rates. The result established in this work improves and extends some existing ones in the literature. Based on the Bahadur-type representation, we further establish the Berry–Esséen …