Trends and Change Points in the Tail Behavior of a Heavy Tailed Distribution
Goedele Dierckx1,2, Jef Teugels2
1Economie en Management, Hogeschool-Universiteit Brussel, Belgium; 2Departement of Mathematics and Leuven Statistics Reasearch Center (LStat), Katholieke Universiteit Leuven, Belgium

We study whether and how the tail behavior of a heavy tailed distribution changes.

Previously we concentrated on testing whether an instantaneous change occurs in the value of the extreme value index gamma. To this end, appropriate test statistics were introduced based on a likelihood approach for independent data.

Now we illustrate with an explicit example that in some cases the extreme value index seems to change gradually rather than instantaneously. Therefor, we discuss trend models together with some diagnostical tools for the extreme value index of heavy tailed distributions.

Finally, a study of the change points in these trends imposes oneself.

Keywords: Change point analysis; Extreme value index; Quantile regression; Maximum likelihood

Biography: Goedele Dierckx graduated with a PhD from the Katholieke Universiteit Leuven, Belgium in 2000. She is currently lecturer in mathematics and statistics at Hogeschool-Universiteit Brussel. Her main areas of research interest are situated in the extreme value statistics. Amongst other subjects, she studied bias reduction methods, multivariate techniques, robust estimation methods, change point analysis in this field.