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标题：Estimating <svg style="vertical-align:-0.0pt;width:16px;" id="M1" height="14.7625" version="1.1" viewBox="0 0 16 14.7625" width="16" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7625)"> <g transform="translate(72,-60.19)"> <text transform="matrix(1,0,0,-1,-71.95,60.24)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝐿</tspan> </text> </g> </g> </svg>-Functionals for Heavy-Tailed Distributions and Application
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作者：Abdelhakim Necir ; Djamel Meraghni
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2010
卷号：2010
DOI：10.1155/2010/707146
出版社：Hindawi Publishing Corporation
摘要：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.