A dynamic mixture model for unsupervised tail estimation without threshold selection

Exceedances over high thresholds are often modeled by fitting a generalized Pareto distribution (GPD) on R+. It is difficult to select the threshold, above which the GPD assumption is enough solid and enough data is available for inference. We suggest a new dynamically weighted mixture model, where...

Full description

Saved in:
Bibliographic Details
Published in:Extremes (Boston) 2002-09, Vol.5 (3), p.219-235
Main Authors: FRIGESSI, Arnoldo, HAUG, Ola, RUE, Havard
Format: Article
Language:English
Subjects:
Applications
Estimating techniques
Exact sciences and technology
Insurance, economics, finance
Mathematical models
Mathematics
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Simulation
Statistical analysis
Statistics
Stochastic processes
Studies
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Exceedances over high thresholds are often modeled by fitting a generalized Pareto distribution (GPD) on R+. It is difficult to select the threshold, above which the GPD assumption is enough solid and enough data is available for inference. We suggest a new dynamically weighted mixture model, where one term of the mixture is the GPD, and the other is a light-tailed density distribution. The weight function varies on R+ in such a way that for large values the GPD component is predominant and thus takes the role of threshold selection. The full data set is used for inference on the parameters present in the two component distributions and in the weight function. Maximum likelihood provides estimates with approximate standard deviations. Our approach has been successfully applied to simulated data and to the (previously studied) Danish fire loss data set. We compare the new dynamic mixture method to Dupuis' robust thresholding approach in peaks-over-threshold inference. We discuss robustness with respect to the choice of the light-tailed component and the form of the weight function. We present encouraging simulation results that indicate that the new approach can be useful in unsupervised tail estimation, especially in heavy tailed situations and for small percentiles. [PUBLICATION ABSTRACT]
ISSN:1386-1999
1572-915X