Computer intensive methods for improving the extremal index estimation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Resampling methodologies have revealed recently as important tools in semi-parametric estimation of parameters in the field of extremes. Among a few parameters of interest, we are here interested in the extremal index, a measure of the degree of local dependence in the extremes of a stationary sequence. Most semi-parametric estimators of this parameter show the same type of behavior: nice asymptotic properties but a high variance for small values of k, the number of upper order statistics used in the estimation and a high bias for large values of k. Two extremal index estimators are here considered: a classical one and a reduced-bias generalized jackknife estimator. Bootstrap and jackknife methodologies are applied for obtaining the "best block size" for resampling and then constructing the bootstrap version of those estimators, that have led to more stable sample paths. A large simulation study was performed for illustrating the behavior of the resampling procedure proposed.
Original languageEnglish
Title of host publicationPROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014
Place of PublicationUSA
PublisherAmerican Institute of Physics Inc.
Pages540005-1–540005-4
Volume1648
ISBN (Print)978-0-7354-1287-3
Publication statusPublished - 2015
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 22 Sep 201428 Sep 2014

Publication series

NameAIP Conference Proceedings
PublisherAmerican Institute of Physics
Volume1648
ISSN (Print)0094-243X

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period22/09/1428/09/14

Keywords

  • Block Bootstrap
  • Extremal index
  • Jackknife
  • Semi-parametric estimation

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