Heavy-Tail Phenomena

DOI10.1007/978-0-387-45024-7zbMath1152.62029OpenAlexW4237850425MaRDI QIDQ5468884

Publication date: 3 May 2006

Published in: Springer Series in Operations Research and Financial Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-387-45024-7

zbMATH Keywords

Karamata representation PRM regularly varying density QQ plot Cramer-Wold device Slutsky's theorem Hill plot Danish data POT method Prohorov theorem Potter bounds infinite-order moving average Kolmogorov convergence criterion multivariate heavy tail acf activity rate almost surely continuous alternative Hill plot Boston University data Breiman theorem crash course exponent of variation infinite-node Poisson model Internet HTTP response data Itô construction Lindley queues one-dimensional convergence one-point uncompactification PP plot QQ estimator second converging together theorem Skorohod convergence Stǎricǎ plot subcone totally skewed vague metric Vervaat's lemma bootstrap functional independence noncompliance Laplace transform convergence weak convergence order statistics decomposition cone asymptotic normality Hausdorff metric fractional Brownian motion Brownian motion regular variation renewal theory metric self-similarity characteristic function augmentation modulus of continuity waiting time ranks topology transformation ARCH domain of attraction least squares compact GARCH long-range dependence partial sum asymptotic independence random walk insurance Poisson process inversion Lévy process quantiles consistent estimator coefficient of tail dependence von Mises condition value-at-risk differentiation autoregressive model Kolmogorov inequality extreme-value theory Radon measure duration moment estimator Pickands estimator diagnostics Pareto distribution autocorrelation Hill estimator ARMA semiparametric empirical measure network model exchange rate marking Poisson transform Arzelà-Ascoli theorem queuing model transmission rate monotone function extremes centering Urysohn lemma hidden regular variation Cauchy auxiliary function binding independent increments exceedance limit theory Mittag-Leffler distribution stochastic continuity heavy-traffic multivariate regular variation local uniform convergence homogeneous Poisson process extremal process transition function subsequence continuous mapping theorem Glivenko-Cantelli theorem stable Lévy motion angular measure limiting measure Donsker's theorem returns compactness condition Laplace functional Portmanteau theorem finite-dimensional convergence time-series models connection rate negative drift vague topology

Mathematics Subject Classification ID

Statistics of extreme values; tail inference (62G32) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics (62-01) Research exposition (monographs, survey articles) pertaining to statistics (62-02) Applications of statistics (62Pxx)

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