Estimating 𝐿-Functionals for Heavy-Tailed Distributions and Application
𝐿-functionals summarize numerous statistical parameters and actuarial risk measures. Their sample estimators are linear combinations of order statistics (𝐿-statistics). There exists a class of heavy-tailed distributions for which the asymptotic normality of these estimators cannot be obtained by cla...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2010/707146 |
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| Summary: | 𝐿-functionals summarize numerous statistical parameters and actuarial risk
measures. Their sample estimators are linear combinations of order statistics
(𝐿-statistics). There exists a class of heavy-tailed distributions for which the
asymptotic normality of these estimators cannot be obtained by classical results.
In this paper we propose, by means of extreme value theory, alternative
estimators for 𝐿-functionals and establish their asymptotic normality. Our
results may be applied to estimate the trimmed 𝐿-moments and financial risk
measures for heavy-tailed distributions. |
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| ISSN: | 1687-952X 1687-9538 |