A Supermartingale Argument for Characterizing the Functional Hill Process Weak Law for Small Parameters

Abstract

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.

Department(s)

Mathematics and Statistics

Comments

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.

Keywords and Phrases

Extreme value theory; Functional Hill process; Supermartingale

International Standard Serial Number (ISSN)

1066-5307; 1934-8045

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2017

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