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Limit theorems for tail processes with application to intermediate quantile estimation
TLDR
In this paper, a description of the weak and strong limiting behaviour of weighted uniform tail empirical and tail quantile processes is given, and the results for the tail quantiles process are applied to obtain weak and strength functional limit theorems for a weighted non-uniform tail-quantile-type process based on a random sample from a distribution that satisfies the so called von Mises sufficient condition for being in the domain of max-attraction of a Frechet distribution.About:
This article is published in Journal of Statistical Planning and Inference.The article was published on 1992-07-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Quantile & Empirical process.read more
Citations
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Journal ArticleDOI
On Smooth Statistical Tail Functionals
TL;DR: In this article, the authors studied the asymptotic behavior of estimators of the extreme value index with a scale and location invariant functional under weak second order conditions on F.
Journal ArticleDOI
On asymptotic normality of the hill estimator
L. de Haan,Sidney I. Resnick +1 more
TL;DR: In this paper, the roles played by smoothness conditions such as Von Mises conditions for the asymptotic normality and gave a minimal condition under which a non constant centering can be used.
Journal ArticleDOI
Second-order regular variation, convolution and the central limit theorem
TL;DR: Second-order regular variation is a refinement of the concept of regular variation which is useful for studying rates of convergence in extreme value theory and asymptotic normality of tail estimators as discussed by the authors.
Journal ArticleDOI
A general class of estimators of the extreme value index
TL;DR: In this paper, the authors consider the class of estimators of the extreme value index β that can be represented as a scale invariant functional T applied to the empirical tail quantile function Qn.
Journal ArticleDOI
Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition
TL;DR: In this article, a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value dis- tribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extremely value distribu- tion is presented.
References
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A Simple General Approach to Inference About the Tail of a Distribution
TL;DR: In this paper, a simple general approach to inference about the tail behavior of a distribution is proposed, which is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference.
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An invariance principle for the law of the iterated logarithm.
Volker Strassen,Volker Strassen +1 more
TL;DR: In this paper, it was shown that with probability one the set of limit points of the sequence (ηn)n≧3 with respect to the uniform topology coincides with the sets of absolutely continuous functions x on "0, 1" such that x(0) = 0, 1, and ηn = 0 for any a ≧ 1.
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Weighted Empirical and Quantile Processes
TL;DR: In this paper, a new Brownian bridge approximation to weighted empirical and quantile processes with rates in probability is introduced, which leads to a number of general invariance theorems for processes indexed by functions.
Journal ArticleDOI
Limit theorems for the ratio of the empirical distribution function to the true distribution function
TL;DR: In this article, the authors considered almost sure limit theorems for a random sample of n uniform (0, 1) random variables and showed that the empirical distribution function converges to 1 a.s.
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Almost sure convergence of the Hill estimator
TL;DR: On caracterise des suites kn de telle facon que l'estimateur de Hill de l'indice de queue base sur les kn statistiques d'ordre superieures d'un echantillon de taille n d'une distribution de Type Pareto soit fortement consistant as mentioned in this paper.