On the favorable estimation for fitting heavy tailed data
On the favorable estimation for fitting heavy tailed data
复制标题
重尾数据拟合的有利估计
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Z. Fabián
中科院分区：
文献类型：
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作者：
M. Stehlík;Rastislav Potockỳ;Helmut Waldl;Z. Fabián
重尾数据及其复合总和的评估在保险、审计和操作风险资本评估等领域有许多应用。在本文中，我们将经典估计器（最大似然估计器、QQ 估计器和矩估计器）与最近引入的“广义中值”、“修剪均值”和基于 t 分数矩的估计器的鲁棒估计器进行了比较。我们推导出同质性似然比检验的精确分布以及二参数 Pareto 模型尾部指数的简单假设。这种精确的测试支持对估计器性能的评估。我们特别讨论了在滥用巴塞尔 II 框架支持的基于对数正态假设的方法时可能遇到的一些问题。真实数据和模拟例子说明了这些方法。
Assessment of heavy tailed data and its compound sums has many applications in insurance, auditing and operational risk capital assessment among others. In this paper, we compare the classical estimators (maximum likelihood, QQ and moment estimators) with the recently introduced robust estimators of “generalized median”, “trimmed mean” and estimators based on t-score moments. We derive the exact distribution of the likelihood ratio tests of homogeneity and simple hypothesis on the tail index of a two-parameter Pareto model. Such exact tests support the assessment of the performance of estimators. In particular, we discuss some problems that one can encounter when misemploying the log-normal assumption based methods supported by the Basel II framework. Real data and simulated examples illustrate the methods.