Bias reduction of a tail index estimator through an external estimation of the second-order parameter

• Type: Article in International Scientific Journal
• Date: 2004

Authors

gomes, mi (Author) Other; caeiro, f (Author) Other; figueiredo, f (Author) FEP

Journal

Title: Statistics

Vol. 38

Pages: 497-510

ISSN: 0233-1888

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 30 Citations

ISI Web of Science

Scopus - 28 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-7N2

DOI: 10.1080/02331880412331284304

Abstract (EN): In this paper, we first consider a class of consistent semi-parametric estimators of a positive tail index gamma, parameterised in a tuning or control parameter alpha. Such a control parameter enables us to have access, for any available sample, to an estimator of the tail index gamma with a null dominant component of asymptotic bias, and consequently with a reasonably flat mean squared error pattern, as a function of k, the number of top-order statistics considered. Such a control parameter depends on a second-order parameter rho, which will be adequately estimated so that we may achieve a high efficiency relative to the classical Hill estimator, provided we use a number of top-order statistics larger than the one usually required for the estimation through the Hill estimator. An illustration of the behaviour of the estimators is provided, through the analysis of the daily log-returns on the Emo-US$ exchange rates.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14