Asymptotic expansion for distribution function of moment estimator for the extreme-value index

2000 ◽  
Vol 43 (11) ◽  
pp. 1131-1143 ◽  
Author(s):  
Jiazhu Pan ◽  
Shihong Cheng
Keyword(s):  
Distribution Function ◽  
Asymptotic Expansion ◽  
Extreme Value ◽  
Extreme Value Index ◽  
Moment Estimator

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>

scholarly journals Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

2021 ◽  
Vol 2068 (1) ◽  
pp. 012003
Author(s):  
Ayari Samia ◽  
Mohamed Boutahar
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Extreme Values ◽  
Empirical Distribution ◽  
Extreme Value ◽  
Dependence Function ◽  
Marginal Distributions ◽  
Nonparametric Estimators ◽  
Monte Carlo Experiments ◽  
Multivariate Extreme Values

Abstract The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

Extreme Values of Waves and Ship Responses Subject to the Markov Chain Condition

1979 ◽  
Vol 23 (03) ◽  
pp. 188-197
Author(s):  
Michel K. Ochi
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Probability Distribution ◽  
Random Process ◽  
Probability Distribution Function ◽  
Extreme Values ◽  
Random Processes ◽  
Chain Condition ◽  
Extreme Value ◽  
Spectral Bandwidth

This paper discusses the effect of statistical dependence of the maxima (peak values) of a stationary random process on the magnitude of the extreme values. A theoretical analysis of the extreme values of a stationary normal random process is made, assuming the maxima are subject to the Markov chain condition. For this, the probability distribution function of maxima as well as the joint probability distribution function of two successive maxima of a normal process having an arbitrary spectral bandwidth are applied to Epstein's theorem for evaluating the extreme values in a given sample under the Markov chain condition. A numerical evaluation of the extreme values is then carried out for a total of 14 random processes, including nine ocean wave records, with various spectral bandwidth parameters ranging from 0.11 to 0.78. From the results of the computations, it is concluded that the Markov concept is applicable to the maxima of random processes whose spectral bandwidth parameter, ɛ, is less than 0.5, and that the extreme values with and without the Markov concept are constant irrespective of the e-value, and the former is approximately 10 percent greater than the latter. It is also found that the sample size for which the extreme value reaches a certain level with the Markov concept is much less than that without the Markov concept. For example, the extreme value will reach a level of 4.0 (nondimensional value) in 1100 observations of the maxima with the Markov concept, while the extreme value will reach the same level in 3200 observations of the maxima without the Markov concept.

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

Asymptotic Expansion for a Class of Sample Quantiles

1982 ◽  
Vol 31 (1-2) ◽  
pp. 1-11
Author(s):  
Kamal C. Chanda
Keyword(s):  
Distribution Function ◽  
Asymptotic Expansion ◽  
Present Article ◽  
Random Sample ◽  
Order Statistic ◽  
Regularity Conditions ◽  
Real Numbers ◽  
Positive Integers ◽  
Sample Quantiles

Let X k: n be the kth order statistic (1 ⩽ k ⩽ n) for a random sample of size n from a population with the distribution function F. Let {α n}, { βn} ( βn > 0) be sequences of real numbers and let { kn} ( kn ⩽ n) be a sequence of positive integers. The present article explores the various choices of α n, βn and kn such that under some mild regularity conditions on F, L( Yn) → n (0,1) as n→∞, where Yn = ( Xkn:n + α n)⁄ βn. It is further shown that under some additional conditions on F, standard asymptotic expansion (in Edgeworth form) for the distribution of Yn can be derived.

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