A Supermartingale Argument for Characterizing the Functional Hill Process Weak Law for Small Parameters
The paper deals with the asymptotic laws of functionals of standard exponential 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.
A. M. Fall et al., "A Supermartingale Argument for Characterizing the Functional Hill Process Weak Law for Small Parameters," Mathematical Methods of Statistics, vol. 26, no. 1, pp. 68 - 80, Springer Verlag, Jan 2017.
The definitive version is available at https://doi.org/10.3103/S1066530717010057
Mathematics and Statistics
Keywords and Phrases
Extreme value theory; Functional Hill process; Supermartingale
International Standard Serial Number (ISSN)
Article - Journal
© 2017 Springer Verlag, All rights reserved.
01 Jan 2017
The two first authors acknowledge support from the World Bank Excellence Center (CEA-MITIC) of Saint-Louis, Senegal, that is continuously funding their research activities starting 2014.