Preface to the Third Edition |
Preface to the Second Edition |
Preface to the First Edition |
The IID Case: Functional Laws of Small Numbers / Part I: |
Functional Laws of Small Numbers / 1: |
Introduction / 1.1: |
Bounds for the Functional Laws of Small Numbers / 1.2: |
Applications / 1.3: |
Extreme Value Theory / 2: |
Domains of Attraction, von Mises Conditions / 2.1: |
The ?-Neighborhood of a GPD / 2.2: |
The Peaks-Over-Threshold Method / 2.3: |
Parameter Estimation in ?-Neighborhoods of GPD / 2.4: |
Initial Estimation of the Class Index / 2.5: |
Power Normalization and p-Max Stable Laws / 2.6: |
Heavy and Super-Heavy Tail Analysis / 2.7: |
Estimation of Conditional Curves / 3: |
Poisson Process Approach / 3.1: |
Applications: The Non-parametric Case / 3.2: |
Applications: The Semiparametric Case / 3.3: |
Extension to Several Points / 3.4: |
A Nearest Neighbor Alternative / 3.5: |
Application: Optimal Accuracy of Estimators / 3.6: |
The IID Case: Multivariate Extremes / Part II: |
Basic Theory of Multivariate Maxima / 4: |
Limiting Distributions of Multivariate Maxima / 4.1: |
Representations and Dependence Functions / 4.2: |
Pickands Representation and Dependence Function / 4.3: |
The D-Norm / 4.4: |
Multivariate Generalized Pareto Distributions / 5: |
The Basics / 5.1: |
Multivariate Peaks-Over-Threshold Approach / 5.2: |
Peaks-Over-Threshold Stability of a GPD / 5.3: |
A Spectral Decomposition Based on Pickands Coordinates / 5.4: |
Multivariate Domains of Attraction, Spectral Neighborhoods / 5.5: |
The Pickands Transform / 5.6: |
Simulation Techniques / 5.7: |
Testing the GPD Assumption, Threshold Selection / 5.8: |
Parametric Estimation Procedures / 5.9: |
Testing in Logistic GPD Models / 5.10: |
The Pickands Approach in the Bivariate Case / 6: |
Preliminaries / 6.1: |
The Measure Generating Function M / 6.2: |
The Pickands Transform in the Bivariate Case / 6.3: |
The Tail Dependence Function / 6.4: |
Testing Tail Dependence against Residual Tail Dependence / 6.5: |
Estimation of the Angular Density in Bivariate GP Models / 6.6: |
Multivariate Extremes: Supplementary Concepts and Results / 7: |
Strong Approximation of Exceedances / 7.1: |
Further Concepts of Extremes / 7.2: |
Thinned Empirical Processes / 7.3: |
Max-Stable Stochastic Processes / 7.4: |
Non-IID Observations / Part III: |
Introduction to the Non-IID Case / 8: |
Definitions / 8.1: |
Stationary Random Sequences / 8.2: |
Independent Random Sequences / 8.3: |
Non-stationary Random Sequences / 8.4: |
Triangular Arrays of Discrete Random Variables / 8.5: |
Extremes of Random Sequences / 9: |
Introduction and General Theory / 9.1: |
Applications: Stationary Sequences / 9.2: |
Applications: Independent Sequences / 9.3: |
Applications: Non-stationary Sequences / 9.4: |
Extensions: Random Fields / 9.5: |
Extremes of Gaussian Processes / 10: |
Stationary Gaussian Processes / 10.1: |
Non-stationary Gaussian Processes / 10.3: |
Application: Empirical Characteristic Functions / 10.4: |
Extensions: Maxima of Gaussian fields / 10.5: |
Extensions for Rare Events / 11: |
Rare Events of Random Sequences / 11.1: |
The Point Process of Exceedances / 11.2: |
Application to Peaks-over-Threshold / 11.3: |
Application to Rare Events / 11.4: |
Triangular Arrays of Rare Events / 11.5: |
Multivariate Extremes of Non-IID Sequences / 11.6: |
Statistics of Extremes / 12: |
Estimation of ? and ?( *) / 12.1: |
Application to Ecological Data / 12.3: |
Frost Data: An Application / 12.4: |
Author Index |
Subject Index |
Bibliography |
Preface to the Third Edition |
Preface to the Second Edition |
Preface to the First Edition |
The IID Case: Functional Laws of Small Numbers / Part I: |
Functional Laws of Small Numbers / 1: |
Introduction / 1.1: |