Censored and extreme losses: Functional convergence and applications to tail goodness-of-fit

IF 2.2 2区 经济学 Q2 ECONOMICS
Martin Bladt, Christoffer Øhlenschlæger
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引用次数: 0

Abstract

This paper establishes the functional convergence of the Extreme Nelson–Aalen and Extreme Kaplan–Meier estimators, which are designed to capture the heavy-tailed behavior of censored losses. The resulting limit representations can be used to obtain the distributions of functionals with respect to the so-called tail process. For instance, we may recover the convergence of a censored Hill estimator, and we further investigate two goodness-of-fit statistics for the tail of the loss distribution. Using the latter limit theorems, we propose two rules for selecting a suitable number of order statistics, both based on test statistics derived from the functional convergence results. The effectiveness of these selection rules is investigated through simulations and an application to a real dataset comprised of French motor insurance claim sizes.
删减损失和极端损失:函数收敛和尾部拟合优度的应用
本文建立了用于捕捉截尾损失的重尾行为的极端Nelson-Aalen和极端Kaplan-Meier估计的泛函收敛性。所得的极限表示可以用来获得关于所谓的尾部过程的泛函分布。例如,我们可以恢复一个被删减的Hill估计量的收敛性,并且我们进一步研究损失分布尾部的两个拟合优度统计量。利用后一个极限定理,我们提出了两个选择合适数量的阶统计量的规则,这两个规则都是基于由泛函收敛结果导出的检验统计量。这些选择规则的有效性通过模拟和应用到一个由法国汽车保险索赔规模组成的真实数据集进行了调查。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Insurance Mathematics & Economics
Insurance Mathematics & Economics 管理科学-数学跨学科应用
CiteScore
3.40
自引率
15.80%
发文量
90
审稿时长
17.3 weeks
期刊介绍: Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.
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