Journal of Statistical Computation and Simulation ( IF 1.2 ) Pub Date : 2021-09-01 , DOI: 10.1080/00949655.2021.1966791 Yi Wu 1 , Wei Yu 2 , Narayanaswamy Balakrishnan 3 , Xuejun Wang 2
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 bound for the modified nonparametric expected shortfall estimator. We show that the optimal rate can achieve nearly under some suitable conditions. We also carry out some numerical simulations and a real data analysis to support the theoretical results established here.
中文翻译:
通过 Bahadur 类型表示和 Berry-Esséen 界限对预期短缺进行非参数估计
预期缺口是金融风险管理中的一项重要风险度量。在本文中,我们研究了改进的非参数预期短缺估计量的 Bahadur 型表示,用于 φ-混合财务损失,对混合率没有任何限制。在这项工作中建立的结果改进并扩展了文献中的一些现有结果。基于 Bahadur 型表示,我们进一步建立了修改后的非参数预期短缺估计量的 Berry-Esséen 界。我们证明了最优速率可以达到几乎在一些合适的条件下。我们还进行了一些数值模拟和真实数据分析,以支持此处建立的理论结果。