本书是Springer《统计系列丛书》之一，全英文版。旨在让读者很好的了解统计中的极值、各种极值模型和极值性质。本书有三大特点：实用性很强。这也本书的最大特点，既讲解了极值模型的基本理论框架，又讲解了实践中运用这些模型的统计推理技巧；理论处理都很基础，运用启发式的例子代替详细的数学证明，对于统计专家和非统计专家同样适用；综合性强，极值模型技巧的方方面面都包含，比如现在仍然运用很广泛的典型古老技巧以及新出现的点过程模型技术等都在本书得到了很好的展示。大量的例子，各种模型程序以及引进一章介绍更深层次的内容，包括贝叶斯定理空间极值。

1 Introduction

1.1 Basic Concepts

1.2 Examples

1.3 Structme of the Book

1.4 Further Reading

2 Basics of Statistical Modeling

2.1 Introduction

2.2 Basic Statistical Concepts

   2.2.1 Random Variables and Their Distributions

   2.2.2 Families of Models

2.3 Multivariate Distributions

2.4 Random Processes

   2.4.1 Stationary Pro(es,,es

   2.4.2 Markov Chains

2.5 Limit Laws

2.6 Parametric Modeling

   2.6.1 The Parametric Framework

   2.6.2 Principles ef Estimaticn

   2.6.3 Maximum Likelihood Estimation

   2.6.4 Approximate Normality cf the Maximum Likelihood Estimator

   2.6.5 Approximate Inference Using the Deviance Function

   2.6.6 Inference Using the Profile Likelihood Function

   2.6.7 Model Diagnostics

2.7 Example

2.8 Further Reading

3 Classical Extreme Value Theory and Models

3.1 Asymptotic Models

   3.1.1 Model Formulation

   3.1.2 Extremal Types Theorem

   3.1.3 The Generalized Extreme Value Distribution

   3.1.4 Outline Proof of the Extremal Types Theorem

   3.1.5 Examples

3.2 Asymptotic Models for Minima

3.3 Inference for the GEV Distribution

   3.3.1 General Considerations

   3.3.2 Maximum Likelihood Estimation

   3.3.3 Inference for Return Levels

   3.3.4 Profile Likelihood

   3.3.5 Model Checking

3.4 Examples

   3.4.1 Annual Maximum Sea-levels at Port Pirie

   3.4.2 Glass Fiber Strength Example

3.5 Model Generalization: the r Largest Order Statistic Model

   3.5.1 Model Formulation

   3.5.2 Modeling the r Largest Order Statistics

   3.5.3 Venice Sea-level Data

3.6 Further Reading

4 Threshold Models

4.1 Introduction

4.2 Asymptotic Model Characterization

   4.2.1 The Generalized Pareto Distribution

   4.2.2 Outline Justification for the Generalized Pareto Model

   4.2.3 Examples

4.3 Modeling Threshold Excesses

   4.3.1 Threshold Selection

   4.3.2 Parameter Estimation

   4.3.3 Return Levels

   4.3.4 Threshold Choice Revisited

   4.3.5 Model Checking

4.4 Examples

   4.4.1 Daily Rainfall Data

   4.4.2 Dow Jones Index Series

4.5 Further Reading

5 Extremes of Dependent Sequences

5.1 Introduction

5.2 Maxima of Stationary Sequences

5.3 Modeling Stationary Series

   5.3.1 Models for Block Maxima

   5.3.2 Threshold Models

   5.3.3 Wooster Temperature Series

   5.3.4 Dow Jones Index Series

5.4 Further Reading

6 Extremes of Non-stationary Sequences

6.1 Model Structures

6.2 Inference

   6.2.1 Parameter Estimation

   6.2.2 Model Choice

   6.2.3 Model Diagnostics

6.3 Examples

   6.3.1 Annual Maximum Sea-levels

   6.3.2 Race Time Data

   6.3.3 Venice Sea-level Data

   6.3.4 Daily Rainfall Data

   6.3.5 Wooster Temperature Data

6.4 Further Reading

7 A Point Process Characterization of Extremes

7.1 Introduction

7.2 Basic Theory of Point Processes

7.3 A Poisson Process Limit for Extremes

   7.3.1 Convergence Law

   7.3.2 Examples

7.4 Connections with Other Extreme Value Models

7.5 Statistical Modeling

7.6 Connections with Threshold Excess Model Likelihood

7.7 Wooster Temperature Series

7.8 Return Level Estimation

7.9 Largest Order Statistic Model

7.10 Further Reading

8 Multivariate Extremes

8.1 Introduction

8.2 Componentwise Maxima

  8.2.1 Asymptotic Characterization

  8.2.2 Modeling

  8.2.3 Example: Annual Maximum Sea-levels

  8.2.4 Structure Variables

8.3 Alternative Representations

  8.3.1 Bivariate Threshold Excess Model

  8.3.2 Point Process Model

  8.3.3 Examples

8.4 Asymptotic Independence

8.5 Further Reading

9 Further Topics

9.1 Bayesian Inference

  9.1.1 General Theory

  9.1.2 Bayesian Inference of Extremes

  9.1.3 Example: Port Pirie Annual Maximum Sea-levels

9.2 Extremes of Markov Chains

9.3 Spatial Extremes

   9.3.1 Max-stable Processes

   9.3.2 Latent Spatial Process Models

9.4 Further Reading

A Computational Aspects

References

Index