Extreme values modelling 绪论

极端值建模和估算是各种应用领域的重要挑战，例如环境，水文，金融，精算科学。

样本的极端部分可能非常重要。也就是说，它可能表现出更大的潜在风险，例如高浓度的空气污染物，洪水，极端索赔规模。

一般而言，极端之建模有三个方面：

1. Univariate Extreme Value Theory:
   单变量极值理论。

2. Bivariate Extreme Value Theory:
   双变量极值理论

3. Multivariate Extreme Value Theory:
   多变量极值理论

与极值相关的绘图：

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经典的书籍以及文章

• E. Gilleland, M. Ribatet, A. Stephenson (2013). A Software Review for Extreme Value Analysis, Extremes , 16 , 103-119.
• R.-D. Reiss, M. Thomas (2007). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields , Springer-Verlag.
• L. de Haan, A. Ferreira (2006). Extreme Value Theory: An Introduction , Springer-Verlag.
• J. Beirlant, Y. Goegebeur, J. Teugels, J. Segers (2004). Statistics of Extremes: Theory and Applications , John Wiley & Sons.
• B. Finkenstaedt, H. Rootzen (2004). Extreme Values in Finance, Telecommunications, and the Environment , Chapman & Hall/CRC.
• S. Coles (2001). An Introduction to Statistical Modeling of Extreme Values , Springer-Verlag.
• P. Embrechts, C. Klueppelberg, T. Mikosch (1997). Modelling Extremal Events for Insurance and Finance , Springer-Verlag.
• S.I. Resnick (1987). Extreme Values, Regular Variation and Point Processes , Springer-Verlag.
• Smith, R.L. (1987). Approximations in extreme value theory. Technical report 205, Center for Stochastic Process, University of North Carolina, 1–34.
• Suveges (2007) Likelihood estimation of the extremal index. Extremes, 10(1), 41-55.
• Suveges and Davison (2010), Model misspecification in peaks over threshold analysis. Annals of Applied Statistics, 4(1), 203-221.