Frick, Melanie: Multivariate extremal density expansions and residual tail dependence structures. 2009
Inhalt
- Danksagung
- Kurzzusammenfassung
- Abstract
- Contents
- List of Special Symbols
- 1 Introduction
- 2 Mathematical basics from multivariate extreme value theory
- 2.1 Extreme value and generalized Pareto distribution functions
- 2.2 Pickands coordinates, spectral decomposition, and Pickands transform
- 2.3 Tail independence and tail dependence
- 3 Multivariate density expansions of finite length
- 4 Testing the tail dependence based on Pickands densities
- 5 Limiting distributions of maxima under triangular schemes
- 5.1 Limiting distributions and residual dependence structures under density expansions
- 5.2 Limiting distributions under a generalized condition
- 5.3 Effects on the power of the test on tail dependence
- 6 Results for other univariate marginal distributions
- 6.1 Basic definitions and results
- 6.2 Spectral densities and Pickands densities
- 6.3 Modified limiting distributions of maxima under triangular schemes
- 7 Measures of asymptotic dependence
- 7.1 Measures of bivariate dependence
- 7.2 Multivariate extensions
- 7.3 The angular tail dependence parameter
- 7.4 Measures of residual dependence under sequences of spectral expansions
- 8 Conclusion and outlook
- Author Index
- Subject Index
- Bibliography