Second-order regular variation, convolution and the central limit theorem

DOI10.1016/S0304-4149(97)00042-2zbMath0913.60001OpenAlexW1967948022MaRDI QIDQ1275940

J. L. Geluk, Laurens De Haan, Sidney I. Resnick, Cătălin Stărică

Publication date: 14 January 1999

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0304-4149(97)00042-2

zbMATH Keywords

convolutionregular variationextreme value theorymaximaHill estimatorsecond-order behaviortail empirical measure

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Characterization and structure theory of statistical distributions (62E10)

Related Items (31)

Asymptotic and finite sample properties of Hill-type estimators in the presence of errors in observations ⋮ Hill's estimator for the tail index of an ARMA model ⋮ Weak properties and robustness of t-Hill estimators ⋮ Second-order asymptotics of tail distortion risk measure for portfolio loss in the multivariate regularly varying model ⋮ The second-order version of Karamata's theorem with applications ⋮ Estimating the conditional tail expectation in the case of heavy-tailed losses ⋮ Extensions of Breiman's theorem of product of dependent random variables with applications to ruin theory ⋮ Second-order asymptotics for convolution of distributions with light tails ⋮ Risk concentration of aggregated dependent risks: the second-order properties ⋮ Tail index estimation, concentration and adaptivity ⋮ Asymptotics of sum of heavy-tailed risks with copulas ⋮ Second order tail asymptotics for the sum of dependent, tail-independent regularly varying risks ⋮ Closure properties of the second-order regular variation under convolutions ⋮ Second-order properties of risk concentrations without the condition of asymptotic smoothness ⋮ Extremal dependence analysis of network sessions ⋮ First and second order asymptotics of the spectral risk measure for portfolio loss under multivariate regular variation ⋮ Second order regular variation and conditional tail expectation of multiple risks ⋮ Robust estimator of conditional tail expectation of Pareto-type distribution ⋮ Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts ⋮ Risk concentration and diversification: second-order properties ⋮ An adaptive optimal estimate of the tail index for MA(1) time series ⋮ Tail asymptotic expansions for \(L\)-statistics ⋮ Risk concentration based on expectiles for extreme risks under FGM copula ⋮ Second-order properties of tail probabilities of sums and randomly weighted sums ⋮ PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION ⋮ The closure property of 2RV under random sum ⋮ THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS ⋮ On tail index estimation based on multivariate data ⋮ Abelian and Tauberian Theorems on the Bias of the Hill Estimator ⋮ Operational risk quantified with spectral risk measures: a refined closed-form approximation ⋮ Tail index estimation for dependent data

Cites Work

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• Tail estimates motivated by extreme value theory
• On the estimation of the extreme-value index and large quantile estimation
• Kernel estimates of the tail index of a distribution
• Second order behaviour of the tail of a subordinated probability distribution
• Weighted empirical and quantile processes
• On asymptotic normality of Hill's estimator for the exponent of regular variation
• A strong invariance theorem for the tail empirical process
• Laws of large numbers for sums of extreme values
• Limit theorems for tail processes with application to intermediate quantile estimation
• Rates of convergence for bivariate extremes
• Tails of subordinated laws: The regularly varying case
• Von Mises-type conditions in second order regular variation
• Second-order regular variation and rates of convergence in extreme-value theory
• The qq-estimator and heavy tails
• The empirical distribution function as a tail estimator
• Central limit theorems for sums of extreme values
• Point processes, regular variation and weak convergence
• Estimating the limit distribution of multivariate extremes
• Smoothing the Hill Estimator
• Asymptotic behavior of hill's estimator for autoregressive data
• Consistency of Hill's estimator for dependent data
• Exact Rates of Convergence to a Stable Law
• Functional central limit theorems for processes with positive drift and their inverses

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