On the accuracy of inference on heavy-tailed distributions

Article

Novak, S. 2013. On the accuracy of inference on heavy-tailed distributions. Theory of Probability and Its Applications. 58 (3), pp. 509-518. https://doi.org/10.1137/S0040585X97986710
TypeArticle
TitleOn the accuracy of inference on heavy-tailed distributions
AuthorsNovak, S.
Abstract

This paper suggests a simple method of deriving nonparametric lower bounds of the accuracy of statistical inference on heavy-tailed distributions. We present lower bounds of the mean squared error of the tail index, the tail constant, and extreme quantiles estimators. The results show that the normalizing sequences of robust estimators must depend in a specific way on the tail index and the tail constant.

PublisherSociety for Industrial and Applied Mathematics
JournalTheory of Probability and Its Applications
ISSN0040-585X
Publication dates
Print2013
Publication process dates
Deposited14 Oct 2015
Accepted01 Jan 2013
Output statusPublished
Accepted author manuscript
Copyright Statement

Published in Theory of Probability & Its Applications in Volume 58, Issue 3, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © 2014 Society of Industrial and Applied Mathematics.

Additional information

Published online: 16 September 2014

Digital Object Identifier (DOI)https://doi.org/10.1137/S0040585X97986710
LanguageEnglish
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