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Nonparametric kernel estimation of expected shortfall under negatively associated sequences

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  • Zhongde Luo
  • Haizhen Meng

Abstract

In this article, Bahadur type expansions of a nonparametric kernel estimator for ES under NA sequences are given. The strong consistency and the uniformly asymptotic normality of the estimator are yielded from the Bahadur type expansions, while the convergence rates of the above asymptotic properties are also obtained. Moreover, the expectation, the variance and the mean squared error (MSE) of the estimator are given. Besides, the optimal bandwidth selection of this estimator is discussed. We point out that all above results are based on the NA sequences. Finally, we conduct numerical simulations and compare performances of some ES estimators.

Suggested Citation

  • Zhongde Luo & Haizhen Meng, 2020. "Nonparametric kernel estimation of expected shortfall under negatively associated sequences," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(11), pages 2749-2769, June.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:11:p:2749-2769
    DOI: 10.1080/03610926.2019.1584303
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