Cormann, Ulf: Statistical models for exceedances with applications to finance and environmental statistics. 2010
Inhalt
- Abstract
- Kurzzusammenfassung
- Danksagung
- Contents
- List of Special Symbols
- Introduction
- Limiting Distributions of Exceedances Under Monotone Transformations
- The Traditional POT--Approach
- A Basic Result Concerning Limiting Distributions
- Continuous g--POT--Stable Distributions
- Some Remarks on Discrete POT-Stable Dfs
- Relations to the Limit Theory of Maxima
- Deriving the Result of Balkema and de Haan
- The Multivariate Case
- Limiting Distributions Under Special Monotone Transformations
- P--POT Stable Distributions
- Limiting Distributions
- Relations to P--Max Stable Laws
- Domains of Attraction of P--POT Stable Distributions
- Mixtures of Regularly Varying Distribution Functions
- The Iterated Case
- Exponential Normalization
- The Log--Pareto Distribution
- The Log--Pareto Model as an Extension of the Pareto Model
- Generalized Log--Pareto Families
- Statistical Inference Within the Log--Pareto Model
- Applications to Real Data
- Conditional Exceedance Point Processes under Covariate Information
- A Short Introduction to Point Processes
- The Basic Point Process Model
- Two Important Examples
- Conditional Distributions in the Poisson Process Case
- Extensions to Dependent Covariates
- Auxiliary Results
- Statistical Inference
- Modeling Upper Tails of Conditional Distributions
- Estimation Using Unconditional Likelihoods
- Conditional Maximum--Likelihood Estimation
- Model Checking
- Likelihood Based Methods in the Literature
- Applications and Simulations
- Moving Thresholds and Multivariate Extensions
- Retrospective, Outlook and Conclusions
- Auxiliary Results
- Documentation of R--Programs
- Bibliography
- Index