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Tail-Index Estimates in Small Samples [PDF]

Journal of Business and Economic Statistics, 2001
Financial returns are known to be nonnormal and tend to have fat-tailed distributions. This article presents a simple methodology that accurately estimates the degree of tail fatness, characterized by the tail index, in small samples. Our method is a weighted average of Hill estimators for different threshold values that corrects for the small-sample ...
Ronald Huisman
exaly   +4 more sources

Simultaneous tail index estimation

Revstat Statistical Journal, 2004
The estimation of the extreme-value index γ based on a sample of independent and identically distributed random variables has received considerable attention in the extreme-value literature.
Jan Beirlant , Yuri Goegebeur
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Dissecting the Multivariate Extremal Index and Tail Dependence

Revstat Statistical Journal, 2020
A central issue in the theory of extreme values focuses on suitable conditions such that the well[1]known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones.
Helena Ferreira , Marta Ferreira
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Distribution and moment characteristics of a quotient of heavy-tailed random variables

Lietuvos Matematikos Rinkinys, 2023
Let us deal with positive i.i.d. random variables X1, . . ., Xm having a tail index α. Calculating a quotient of two biggest members in the set, we obtain a new random variable and investigate its distribution and moment properties.
Kęstutis Gadeikis
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Regression Estimator for the Tail Index [PDF]

Journal of Statistical Theory and Practice, 2020
AbstractEstimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate this parameter. Several recent publications’ aim was to improve the Hill estimator, using different methods, for example the bootstrap, or the Kolmogorov–Smirnov ...
László Németh, András Zempléni
openaire   +3 more sources

Dimension reduction for the estimation of the conditional tail index

Scandinavian Journal of Statistics
ABSTRACTWe are interested in the relationship between the large values of a real random variable and its associated multidimensional covariate, in the context where the conditional distribution is heavy‐tailed. Estimating the positive conditional tail index of a heavy‐tailed conditional distribution is a crucial step for statistical inference, but the ...
Laurent Gardes
exaly   +4 more sources

Extreme Value Statistics for Evolving Random Networks

Mathematics, 2023
Our objective is to survey recent results concerning the evolution of random networks and related extreme value statistics, which are a subject of interest due to numerous applications.
Natalia Markovich, Marijus Vaičiulis
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Semiparametric Tail Index Regression [PDF]

Journal of Business & Economic Statistics, 2020
Abstract–Understanding why extreme events occur is often of major scientific interest in many fields. The occurrence of these events naturally depends on explanatory variables, but there is a severe lack of flexible models with asymptotic theory for understanding this dependence, especially when variables can affect the outcome nonlinearly.
Rui Li, Chenlei Leng, Jinhong You
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On Max-Semistable Laws and Extremes for Dynamical Systems

Entropy, 2021
Suppose (f,X,μ) is a measure preserving dynamical system and ϕ:X→R a measurable observable. Let Xi=ϕ∘fi−1 denote the time series of observations on the system, and consider the maxima process Mn:=max{X1,…,Xn}.
Mark P. Holland, Alef E. Sterk
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Smooth tail-index estimation [PDF]

Journal of Statistical Computation and Simulation, 2009
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0]. Replacing the order statistics in tail index estimators by their corresponding quantiles from the distribution function ...
Müller, S, Rufibach, K
openaire   +3 more sources