Statistics of extremes by oracle estimation

DOI10.1214/07-AOS535zbMath1282.62131arXiv0808.0976MaRDI QIDQ939657

Vladimir Spokoiny, I. G. Grama

Publication date: 28 August 2008

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

Full work available at URL: https://arxiv.org/abs/0808.0976

zbMATH Keywords

extreme valuesHill estimatorhigh quantilesnonparametric adaptive estimationprobabilities of rare events

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Nonparametric estimation (62G05) Statistics of extreme values; tail inference (62G32)

Related Items

Truncated estimation of ratio statistics with application to heavy tail distributions, Cyber risk frequency, severity and insurance viability, A modeler's guide to extreme value software, Tail index estimation, concentration and adaptivity, Rejoinder on: ``Local quantile regression, Estimation of the survival probabilities by adjusting a Cox model to the tail, Uniform in bandwidth consistency of kernel estimators of the tail index, Estimation of extreme survival probabilities with cox model, Nonparametric adaptive estimation of conditional probabilities of rare events and extreme quantiles, Multiscale local change point detection with applications to value-at-risk

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems
• Best attainable rates of convergence for estimates of parameters of regular variation
• Adaptive estimates of parameters of regular variation
• Laws of large numbers for sums of extreme values
• Approximate distributions of order statistics. With applications to nonparametric statistics
• A simple general approach to inference about the tail of a distribution
• Heavy tail modeling and teletraffic data. (With discussions and rejoinder)
• The bootstrap methodology in statistics of extremes -- choice of optimal sample fraction
• Selecting the optimal sample fraction in univariate extreme value estimation
• Optimal rates of convergence for estimates of the extreme value index
• Local adaptation to inhomogeneous smoothness: Resolution level
• Estimation of Parameters and Larger Quantiles Based on the k Largest Observations
• Ideal spatial adaptation by wavelet shrinkage
• Statistics of Extremes
• Using a bootstrap method to choose the sample fraction in tail index estimation