Lower bounds to the accuracy of inference on heavy tails

Novak, Serguei (2014) Lower bounds to the accuracy of inference on heavy tails. Bernoulli, 20 (2). pp. 979-989. ISSN 1350-7265

PDF - Final accepted version (with author's formatting)
Download (155kB) | Preview


The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if α^n is an estimator of the tail index αP and {zn} is a sequence of positive numbers such that supP∈DrP(|α^n−αP|≥zn)→0, where Dr is a certain class of heavy-tailed distributions, then zn≫n−r. The paper presents a non-asymptotic lower bound to the probabilities P(|α^n−αP|≥zn). We also establish non-uniform lower bounds to the accuracy of tail constant and extreme quantiles estimation. The results reveal that normalising sequences of robust estimators should depend in a specific way on the tail index and the tail constant.

Item Type: Article
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 18125
Useful Links:
Depositing User: Serguei Novak
Date Deposited: 14 Oct 2015 09:55
Last Modified: 07 Dec 2018 08:35
URI: http://eprints.mdx.ac.uk/id/eprint/18125

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year