A supermartingale argument for characterizing the Functional Hill process weak law for small parameters
Methodology
2016-11-22 v4
Abstract
The paper deals with the asymptotic laws of functional of standard random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in the Weibull domain of attraction. We use techniques based on martingales theory to describe the non Gaussian asymptotic distribution of the aforementioned statistics. We provide results of a simulation study as well as statistical tests that may be of interest with the proposed results.
Keywords
Cite
@article{arxiv.1306.5462,
title = {A supermartingale argument for characterizing the Functional Hill process weak law for small parameters},
author = {Gane Samb Lo and Adja Mbarka Fall and Cheikhna Hamallah Ndiaye and Akym Adekpejou},
journal= {arXiv preprint arXiv:1306.5462},
year = {2016}
}
Comments
25 pages. arXiv admin note: text overlap with arXiv:1208.1487, Submitted under the title : On The Weak Convergence Of The Functional Hill Process For Small Parameters, Ti be published in Mathematical Methods of Statistics 2017