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Title: Extreme Value Theory——An Introduction

Authors: Laurens de Haan,  Ana Ferreira

Total Page: 415

Publisher: Springer

Contents:

Preface vii
List of Abbreviations and Symbols xv
Part I One-Dimensional Observations
1 Limit Distributions and Domains of Attraction 3
1.1 Extreme Value Theory: Basics 3
1.1.1 Introduction 3
1.1.2 Alternative Formulations of the Limit Relation 4
1.1.3 Extreme Value Distributions 6
1.1.4 Interpretation of the Alternative Conditions; Case Studies .. 12
1.1.5 Domains of Attraction: A First Approach 14
1.2 Domains of Attraction 19
Exercises 34
2 Extreme and Intermediate Order Statistics 37
2.1 Extreme Order Statistics and Poisson Point Processes 37
2.2 Intermediate Order Statistics 40
2.3 Second-Order Condition 43
2.4 Intermediate Order Statistics and Brownian Motion 49
Exercises 60
3 Estimation of the Extreme Value Index and Testing 65
3.1 Introduction 65
3.2 A Simple Estimator for the Tail Index (y > 0): The Hill Estimator . 69
3.3 General Case y e E: The Pickands Estimator 83
3.4 The Maximum Likelihood Estimator (y > — \) 89
3.5 AMomentEstimator (/