Nonparametric estimation of expected shortfall for α-mixing financial losses

Xuejun Wang, Yi Wu and Wei Wang ()
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Xuejun Wang: Anhui University
Yi Wu: Chizhou University
Wei Wang: Chizhou University

Computational Statistics, 2024, vol. 39, issue 6, No 12, 3157-3179

Abstract: Abstract In this paper, we investigate the Bahadur type representation of a nonparametric expected shortfall estimator for $$\alpha $$ α -mixing financial losses. Based on the Bahadur type representation, we further establish the Berry–Esseen bound of the nonparametric expected shortfall estimator. It is shown that the optimal rate can achieve nearly $$O(n^{-1/8})$$ O ( n - 1 / 8 ) under some appropriate conditions. We also carry out some numerical simulations and a real data example to support our theoretical results based on finite samples.

Keywords: Bahadur type representation; Berry–Esseen bound; Nonparametric estimation; Expected shortfall; $$\alpha $$ α -mixing (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01434-5

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