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Nonparametric estimation of conditional expectile-based risk measures

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Abstract

This article discusses nonparametric estimation of some conditional expectile-based risk measures using local polynomial fitting. The focus is on estimating conditional expectile-based Value-at-Risk and conditional expectile-based Expected Shortfall. Estimation of the latter is also discussed in a framework of heavy-tailed distributions, which involves a data-driven choice of the number of tail observations used in the estimation. The finite-sample performance of the proposed conditional risk measure estimators is investigated in a simulation study. The practical use of the developed methods is illustrated in three real data examples.

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Acknowledgements

The authors thank the editor, an associate editor and the reviewers for their valuable comments that led to an improvement of the paper.

Funding

The authors gratefully acknowledge support from the Flemish Science Foundation [Research GrantFWO G0D6619N] and from Research Fund KU Leuven [C16/20/002 project].

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  1. Department of Mathematics, KU Leuven, Celestijnenlaan 200B, PO Box 2400, 3001, Leuven, Heverlee, Belgium

    C. Adam & I. Gijbels

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  1. C. Adam
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  2. I. Gijbels
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Correspondence to I. Gijbels.

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Numerical experiments have been carried out using the R packages mentioned in the text. Data sets are publicly available, and url addresses for these are included in the text.

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Adam, C., Gijbels, I. Nonparametric estimation of conditional expectile-based risk measures. Stat Methods Appl 34, 939–977 (2025). https://doi.org/10.1007/s10260-025-00807-y

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