Afrika Statistika
- Afr. Stat.
- Volume 13, Number 3 (2018), 1795-1822.
A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory
Gane Samb Lo, Adja Mbarka Fall, and Harouna Sangaré
Abstract
Consider the following demimartingale \begin{equation*} \sum_{j=1}^{k-1}f(j)(\exp (-\gamma \sum_{h=j+1}^{k-1}E_{h}/h)-\exp (-\gamma \sum_{h=j}^{k-1}E_{h}/h)), \end{equation*} where \(E_{1},E_{2},...\) are independent standard exponential random variables, \(\gamma>0\), \(k\) is a positive integer and \(f(j)\) is an increasing function of the integer $j\geq1$. We find general conditions under which the central limit theorem (CLT) holds and next apply the results to find the asymptotic behavior of the functional Hill within the Extreme Value Theory (EVT) field. This results show a new trend for the central limit theorem issue for non-stationary sequences of associated variables.
Article information
Source
Afr. Stat., Volume 13, Number 3 (2018), 1795-1822.
Dates
First available in Project Euclid: 12 December 2018
Permanent link to this document
https://projecteuclid.org/euclid.as/1544583716
Digital Object Identifier
doi:10.16929/as/1795.134
Mathematical Reviews number (MathSciNet)
MR3887184
Zentralblatt MATH identifier
07003217
Subjects
Primary: 62E20: Asymptotic distribution theory 62F12: Asymptotic properties of estimators 60F05: Central limit and other weak theorems
Secondary: 60B10: Convergence of probability measures 60F17: Functional limit theorems; invariance principles
Keywords
Extreme value theory Associated random variables demimartingales asymptotic laws functional Hill processes extreme value theory statistical tests
Citation
Lo, Gane Samb; Fall, Adja Mbarka; Sangaré, Harouna. A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory. Afr. Stat. 13 (2018), no. 3, 1795--1822. doi:10.16929/as/1795.134. https://projecteuclid.org/euclid.as/1544583716