Limit theorems for tail processes with application to intermediate quantile estimation

DOI10.1016/0378-3758(92)90156-MzbMath0759.60017MaRDI QIDQ1200019

John H. J. Einmahl

Publication date: 17 January 1993

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

zbMATH Keywords

weight functionFréchet distributiontail empirical and tail quantile process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Nonparametric tolerance and confidence regions (62G15) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (13)

Inference for intermediate Haezendonck-Goovaerts risk measure ⋮ Estimating the Mean of Heavy-tailed Distribution under Random Truncation ⋮ A general class of estimators of the extreme value index ⋮ The tail empirical process for long memory stochastic volatility sequences ⋮ INFERENCE ON TWO-COMPONENT MIXTURES UNDER TAIL RESTRICTIONS ⋮ Change-Point Tests for the Tail Parameter of Long Memory Stochastic Volatility Time Series ⋮ Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition ⋮ Weak convergence of the tail empirical process for dependent sequences ⋮ On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation ⋮ Jackknife method for intermediate quantiles ⋮ Second-order regular variation, convolution and the central limit theorem ⋮ The tail empirical process for long memory stochastic volatility models with leverage ⋮ Nonparametric estimation of the spectral measure of an extreme value distribution.

Cites Work

• Weighted empirical and quantile processes
• On the tail behaviour of quantile processes
• Laws of the iterated logarithm in the tails for weighted uniform empirical processes
• Strong limit theorems for weighted quantile processes
• A strong invariance theorem for the tail empirical process
• The a.s. behavior of the weighted empirical process and the LIL for the weighted tail empirical process
• A simple general approach to inference about the tail of a distribution
• Approximation of intermediate quantile processes
• Nonstandard functional laws of the iterated logarithm for tail empirical and quantile processes
• The empirical distribution function as a tail estimator
• Almost sure convergence of the Hill estimator
• Limit theorems for the ratio of the empirical distribution function to the true distribution function
• An invariance principle for the law of the iterated logarithm

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