A note on the asymptotic variance at optimal levels of a bias-corrected Hill estimator

M. Ivette Gomes, Dinis Pestana and Frederico Caeiro

Statistics & Probability Letters, 2009, vol. 79, issue 3, 295-303

Abstract: For heavy tails, with a positive tail index [gamma], classical tail index estimators, like the Hill estimator, are known to be quite sensitive to the number of top order statistics k used in the estimation, whereas second-order reduced-bias estimators show much less sensitivity to changes in k. In the recent minimum-variance reduced-bias (MVRB) tail index estimators, the estimation of the second order parameters in the bias has been performed at a level k1 of a larger order than that of the level k at which we compute the tail index estimators. Such a procedure enables us to keep the asymptotic variance of the new estimators equal to the asymptotic variance of the Hill estimator, for all k at which we can guarantee the asymptotic normality of the Hill statistics. These values of k, as well as larger values of k, will also enable us to guarantee the asymptotic normality of the reduced-bias estimators, but, to reach the minimal mean squared error of these MVRB estimators, we need to work with levels k and k1 of the same order. In this note we derive the way the asymptotic variance varies as a function of q, the finite limiting value of k/k1, as the sample size n increases to infinity.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00401-X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:79:y:2009:i:3:p:295-303

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().