英文标题：
《Data and uncertainty in extreme risks - a nonlinear expectations
approach》
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作者：
Samuel N. Cohen
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最新提交年份：
2018
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英文摘要：
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a heavy-tailed context (in particular when our data are described by a Pareto distribution, as is common in much of extreme value theory), the theory of [5] is insufficient, and requires an additional regularization step which we introduce. By asking whether this regularization is possible, we obtain a qualitative requirement for reliable estimation of tail quantities and risk measures, in a Pareto setting.
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中文摘要：
尾部数量的估计，如预期短缺或风险价值，是一个困难的问题。我们展示了非线性期望理论，尤其是文献[5]中引入的数据稳健期望，如何帮助量化这些问题的统计不确定性。然而，当我们处于重尾环境中时（尤其是当我们的数据由帕累托分布描述时，这在许多极值理论中很常见），文献[5]的理论是不够的，需要我们引入一个额外的正则化步骤。通过询问这种正则化是否可行，我们获得了在帕累托环境下可靠估计尾部数量和风险度量的定性要求。
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分类信息：

一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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