Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions
A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorise...
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| Format: | Article |
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Elsevier
2018
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| Online Access: | https://eprints.nottingham.ac.uk/41195/ |
| _version_ | 1848796218893795328 |
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| author | El Methni, Jonathan Stupfler, Gilles |
| author_facet | El Methni, Jonathan Stupfler, Gilles |
| author_sort | El Methni, Jonathan |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorised versions of the empirical counterparts of extreme analogues of Wang distortion risk measures are considered. Their asymptotic properties are analysed, and it is shown that it is possible to construct corrected versions of trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in difficult finite-sample situations when the underlying distribution has a very heavy right tail. This technique is showcased on a set of real fire insurance data. |
| first_indexed | 2025-11-14T19:44:30Z |
| format | Article |
| id | nottingham-41195 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:44:30Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-411952020-05-04T19:34:18Z https://eprints.nottingham.ac.uk/41195/ Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions El Methni, Jonathan Stupfler, Gilles A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorised versions of the empirical counterparts of extreme analogues of Wang distortion risk measures are considered. Their asymptotic properties are analysed, and it is shown that it is possible to construct corrected versions of trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in difficult finite-sample situations when the underlying distribution has a very heavy right tail. This technique is showcased on a set of real fire insurance data. Elsevier 2018-04-30 Article PeerReviewed El Methni, Jonathan and Stupfler, Gilles (2018) Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions. Econometrics and Statistics, 6 . pp. 129-148. ISSN 2452-3062 Asymptotic normality Extreme value statistics Heavy-tailed distribution Trimming Wang distortion risk measure Winsorising http://www.sciencedirect.com/science/article/pii/S2452306217300151 doi:10.1016/j.ecosta.2017.03.002 doi:10.1016/j.ecosta.2017.03.002 |
| spellingShingle | Asymptotic normality Extreme value statistics Heavy-tailed distribution Trimming Wang distortion risk measure Winsorising El Methni, Jonathan Stupfler, Gilles Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title | Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title_full | Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title_fullStr | Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title_full_unstemmed | Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title_short | Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions |
| title_sort | improved estimators of extreme wang distortion risk measures for very heavy-tailed distributions |
| topic | Asymptotic normality Extreme value statistics Heavy-tailed distribution Trimming Wang distortion risk measure Winsorising |
| url | https://eprints.nottingham.ac.uk/41195/ https://eprints.nottingham.ac.uk/41195/ https://eprints.nottingham.ac.uk/41195/ |