英文标题：
《On the Super-Additivity and Estimation Biases of Quantile Contributions》
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作者：
Nassim N Taleb, Raphael Douady
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最新提交年份：
2014
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英文摘要：
  Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.
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中文摘要：
对总（浓度）的上百分位贡献的样本度量是向下倾斜的、不稳定的估计量，对样本量极为敏感，在解释大偏差时呈凹形。这使得它们特别不适用于具有幂律尾的领域，尤其是指数值较低的领域。如本文所示，这些估计器可以随着时间的推移而变化，并随着人口规模的增加而增加，从而提供了集中度结构变化的假象。在聚集分布和混合分布下，它们也不一致，因为A和B浓度测量的加权平均值往往低于A和B的加权平均值。此外，可以证明，在这种厚尾情况下，总总和的增加需要伴随浓度测量样本量的增加。我们研究了齐次分布和混合分布下的估计超加性和偏差。
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分类信息：

一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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