Which Extreme Values are Really Extremes?
The aim of this paper is to give a formal definition and consistent estimates of the extremes of a population. This definition relies on a threshold value that delimits the extremes and on the uniform convergence of the distribution of these extremes to a Pareto type distribution. The tail parameter of this Pareto type distribution is the tail index of the data distribution. The estimator of the threshold is anchored in the Kolmogorov-Smirnov distance between consistent estimates of those two distributions. Our estimator is consistent and via the construction of confidence intervals for the tail index (derived from our threshold estimator) we overcome the bias problems of the usual tail index estimators (Hill or Pickands). The paper also explores the validity of our definition for standard sample sizes. For this purpose, a hypothesis test is designed in order to reject extremes estimates that are not really extremes. Applications for different stock returns are presented
|Date of creation:||11 Aug 2004|
|Date of revision:|
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:ecm:nawm04:144. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.