Tail estimates motivated by extreme value theory

DOI10.1214/aos/1176346804zbMath0555.62035OpenAlexW2063062722MaRDI QIDQ760731

Publication date: 1984

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176346804

zbMATH Keywords

order statistics regular variation rates of convergence Pareto distribution tail estimation empirical mean residual life log transformed data

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Nonparametric estimation (62G05) Order statistics; empirical distribution functions (62G30)

Related Items

Asymptotic and finite sample properties of Hill-type estimators in the presence of errors in observations ⋮ Central limit theorems for sums of extreme values ⋮ Extreme quantile estimation in \(\delta\)-neighborhoods of generalized Pareto distributions ⋮ On the asymptotic joint distribution of an unbounded number of sample extremes ⋮ The mean residual life function at great age: Applications to tail estimation ⋮ When are intermediate processes of the same stochastic order? ⋮ Approximation to the expectation of a function of order statistics and its applications ⋮ The empirical distribution function as a tail estimator ⋮ On robust tail index estimation for linear long-memory processes ⋮ A general class of estimators of the extreme value index ⋮ Asymptotically efficient estimation of the index of regular variation ⋮ Extremal memory of stochastic volatility with an application to tail shape inference ⋮ On an improvement of Hill and some other estimators ⋮ EXTREME VALUE ANALYSIS WITHOUT THE LARGEST VALUES: WHAT CAN BE DONE? ⋮ Estimating asymptotic dependence functionals in multivariate regularly varying models ⋮ On tail index estimation using a sample with missing observations ⋮ The harmonic moment tail index estimator: asymptotic distribution and robustness ⋮ Comparison of estimation methods in extreme value theory ⋮ On the asymptotic normality of Hill's estimator ⋮ Extremal dependence analysis of network sessions ⋮ On optimal portfolio diversification with respect to extreme risks ⋮ Asymptotic normality of the ET method -- application to the ET test ⋮ Simple tail index estimation for dependent and heterogeneous data with missing values ⋮ Test for the existence of finite moments via bootstrap ⋮ Tail fit and the Zipf-Pareto law ⋮ Reiss and Thomas' automatic selection of the number of extremes ⋮ On estimation of the exponent of regular variation using a sample with missing observations ⋮ Pareto Index Estimation Under Moderate Right Censoring ⋮ Using a bootstrap method to choose the sample fraction in tail index estimation ⋮ ON TAIL INDEX ESTIMATION FOR DEPENDENT, HETEROGENEOUS DATA ⋮ On univariate extreme value statistics and the estimation of reinsurance premiums ⋮ Residual estimators ⋮ Extremes of projections of functional time series on data-driven basis systems ⋮ Parameter Estimation of Stable Distributions ⋮ Statistical modeling of spatial extremes ⋮ Corrected phase-type approximations of heavy-tailed risk models using perturbation analysis ⋮ Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions ⋮ On tail index estimation based on multivariate data ⋮ Estimating the parameters of rare events ⋮ Second-order regular variation, convolution and the central limit theorem ⋮ Econometric modeling of risk measures: a selective review of the recent literature ⋮ Regression estimator for the tail index ⋮ Prediction of record values ⋮ On the distribution of tail array sums for strongly mixing stationary sequences ⋮ Tail index estimation for dependent data ⋮ Bootstrap confidence intervals for the pareto index ⋮ Effect of extrapolation on coverage accuracy of prediction intervals computed from Pareto-type data ⋮ Estimation of the index parameter for autoregressive data using the estimated innovations ⋮ A PARAMETRIC BOOTSTRAP FOR HEAVY-TAILED DISTRIBUTIONS ⋮ An Estimator of the Exponent of Regular Variation Based on K-Record Values ⋮ Robust confidence bounds for extreme upper quantiles ⋮ High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression ⋮ Optimal asymptotic estimation of small exceedance probabilities ⋮ Estimation of distribution tails —a semiparametric approach ⋮ A class of location invariant estimators for heavy tailed distributions ⋮ An exploratory first step in teletraffic data modeling: evaluation of long-run performance of parameter estimators.