On the impossibility of estimating densities in the extreme tail

DOI10.1016/S0167-7152(98)00246-6zbMath0916.62031MaRDI QIDQ1284587

Jan Beirlant, Luc P. Devroye

Publication date: 31 May 1999

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

rate of convergenceextreme valueslower boundsmaxima

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items (6)

Unnamed Item ⋮ Impossibility of consistent estimation of the distribution function of a sample maximum ⋮ Nonparametric estimation of the coefficient of overlapping-theory and empirical application ⋮ On the controversy over tailweight of distributions. ⋮ On consistent and rate optimal estimation of the missing mass ⋮ On the use of the peaks over thresholds method for estimating out-of-sample quantiles.

Cites Work

• Unnamed Item
• Best attainable rates of convergence for estimates of parameters of regular variation
• On the estimation of the extreme-value index and large quantile estimation
• Kernel estimates of the tail index of a distribution
• Statistical inference using extreme order statistics
• A simple general approach to inference about the tail of a distribution
• On the estimation of extreme tail probabilities
• Another proof of a slow convergence result of Birgé
• Second-order regular variation and rates of convergence in extreme-value theory
• Refined Pickands estimators of the extreme value index
• On estimating a density using Hellinger distance and some other strange facts
• On arbitrarily slow rates of global convergence in density estimation
• Probability Inequalities for Sums of Bounded Random Variables

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