Bias reduction and explicit semi-parametric estimation of the tail index

DOI10.1016/S0378-3758(03)00205-2zbMath1047.62045MaRDI QIDQ1878667

M. Ivette Gomes, M. João Martins

Publication date: 8 September 2004

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

zbMATH Keywords

tablessimulationsextremesfinite sample properties

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05) Statistics of extreme values; tail inference (62G32) Monte Carlo methods (65C05)

Related Items (33)

Robust and bias-corrected estimation of the probability of extreme failure sets ⋮ Bias correction in extreme value statistics with index around zero ⋮ Asymptotically best linear unbiased tail estimators under a second-order regular variation condition ⋮ Kernel-type estimators for the distortion risk premiums of heavy-tailed distributions ⋮ Bias reduction in risk modelling: semi-parametric quantile estimation ⋮ On robust tail index estimation ⋮ Robust nonparametric estimation of the conditional tail dependence coefficient ⋮ Robust estimation of the conditional stable tail dependence function ⋮ Bias reduction for endpoint estimation ⋮ Location invariant Weiss-Hill estimator ⋮ A class of unbiased location invariant Hill-type estimators for heavy tailed distributions ⋮ Reduced-bias estimator of the Proportional Hazard Premium for heavy-tailed distributions ⋮ Asymptotic normality of location invariant heavy tail index estimator ⋮ An estimator of heavy tail index through the generalized jackknife methodology ⋮ Estimation of extreme quantiles from heavy-tailed distributions in a location-dispersion regression model ⋮ Local Estimation of the Second-Order Parameter in Extreme Value Statistics and Local Unbiased Estimation of the Tail Index ⋮ Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence ⋮ A review of more than one hundred Pareto-tail index estimators ⋮ Comparing extreme models when the sign of the extreme value index is known ⋮ Improved reduced-bias tail index and quantile estimators ⋮ A simple second-order reduced bias’ tail index estimator ⋮ Bias reduction for high quantiles ⋮ Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution ⋮ Reduced‐bias tail index estimation and the jackknife methodology ⋮ Goodness-of-fit testing for Weibull-type behavior ⋮ Local robust estimation of Pareto-type tails with random right censoring ⋮ Kernel-type estimator of the reinsurance premium for heavy-tailed loss distributions ⋮ A heuristic adaptive choice of the threshold for bias-corrected Hill estimators ⋮ Does bias reduction with external estimator of second order parameter work for endpoint? ⋮ Reduced-Bias Tail Index Estimators Under a Third-Order Framework ⋮ Tail Index Estimation for Heavy-Tailed Models: Accommodation of Bias in Weighted Log-Excesses ⋮ Second-order refined peaks-over-threshold modelling for heavy-tailed distributions ⋮ Bias-corrected estimation for conditional Pareto-type distributions with random right censoring

Cites Work

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• Adaptive estimates of parameters of regular variation
• A simple general approach to inference about the tail of a distribution
• The bootstrap methodology in statistics of extremes -- choice of optimal sample fraction
• ``Asymptotically unbiased estimators of the tail index based on external estimation of the second order parameter
• Tail index estimation and an exponential regression model
• Generalized jackknife semi-parametric estimators of the tail index
• Estimating a tail exponent by modelling departure from a Pareto distribution
• Comparison of tail index estimators
• Maximum likelihood revisited under a semi-parametric context - estimation of the tail index
• Generalizations of the Hill estimator -- asymptotic versus finite sample behaviour
• Alternatives to a semi-parametric estimator of parameters of rare events -- the jackknife methodology

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