Peaks Over Random Threshold Asymptotically Best Linear Estimation of the Extreme Value Index

2014 ◽  
pp. 145-153
Author(s):  
Lígia Henriques-Rodrigues ◽  
M. Ivette Gomes
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Linear Estimation ◽  
Random Threshold

scholarly journals A moment estimator for the conditional extreme-value index

2013 ◽  
Vol 7 (0) ◽  
pp. 2298-2343 ◽  
Author(s):  
Gilles Stupfler
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Moment Estimator

scholarly journals A Double-indexed Functional Hill Process and Applications

2016 ◽  
Vol 8 (4) ◽  
pp. 144
Author(s):  
Modou Ngom ◽  
Gane Samb Lo
Keyword(s):  
Stochastic Process ◽  
Distribution Function ◽  
Asymptotic Behaviour ◽  
Stochastic Processes ◽  
Order Statistics ◽  
Finite Dimension ◽  
Domain Of Attraction ◽  
Extreme Value ◽  
Extreme Value Index

<div>Let $X_{1,n} \leq .... \leq X_{n,n}$ be the order statistics associated with a sample $X_{1}, ...., X_{n}$ whose pertaining distribution function (\textit{df}) is $F$. We are concerned with the functional asymptotic behaviour of the sequence of stochastic processes</div><div> </div><div>\begin{equation}<br />T_{n}(f,s)=\sum_{j=1}^{j=k}f(j)\left( \log X_{n-j+1,n}-\log<br />X_{n-j,n}\right)^{s} ,  \label{fme}<br />\end{equation}</div><div> </div><div>indexed by some classes $\mathcal{F}$ of functions $f:\mathbb{N}%^{\ast}\longmapsto \mathbb{R}_{+}$ and $s \in ]0,+\infty[$ and where $k=k(n)$ satisfies</div><div> </div><div>\begin{equation*}<br />1\leq k\leq n,k/n\rightarrow 0\text{ as }n\rightarrow \infty .<br />\end{equation*}</div><div> </div><div>We show that this is a stochastic process whose margins generate estimators of the extreme value index when $F$ is in the extreme domain of attraction. We focus in this paper on its finite-dimension asymptotic law and provide a class of new estimators of the extreme value index whose performances are compared to analogous ones. The results are next particularized for one explicit class $\mathcal{F}$.</div>

Comparing extreme models when the sign of the extreme value index is known

2010 ◽  
Vol 80 (7-8) ◽  
pp. 739-746 ◽  
Author(s):  
Deyuan Li ◽  
Liang Peng
Keyword(s):  
Extreme Value ◽  
Extreme Value Index

scholarly journals Minimum‐variance reduced‐bias estimation of the extreme value index: A theoretical and empirical study

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Frederico Caeiro ◽  
Lígia Henriques‐Rodrigues ◽  
M. Ivette Gomes ◽  
Ivanilda Cabral
Keyword(s):  
Empirical Study ◽  
Minimum Variance ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Bias Estimation

scholarly journals Refined Pickands estimators of the extreme value index

1995 ◽  
Vol 23 (6) ◽  
pp. 2059-2080 ◽  
Author(s):  
Holger Drees
Keyword(s):  
Extreme Value ◽  
Extreme Value Index

Mean-of-order p reduced-bias extreme value index estimation under a third-order framework

Extremes ◽  
2016 ◽  
Vol 19 (4) ◽  
pp. 561-589 ◽  
Author(s):  
Frederico Caeiro ◽  
M. Ivette Gomes ◽  
Jan Beirlant ◽  
Tertius de Wet
Keyword(s):  
Extreme Value ◽  
Extreme Value Index ◽  
Third Order ◽  
Index Estimation
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