Asymptotically best linear unbiased tail estimators under a second-order regular variation condition

• Type: Article in International Scientific Journal
• Date: 2005

Authors

gomes, mi (Author) Other; figueiredo, f (Author) FEP; mendonca, s (Author) Other

Journal

Title: Journal of Statistical Planning and Inference

Vol. 134 No. 2

Pages: 409-433

ISSN: 0378-3758

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 23 Citations

Scopus - 25 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-15N

DOI: 10.1016/j.jspi.2004.04.013

Abstract (EN): For regularly varying tails, estimation of the index of regular variation, or tail index, gamma, is often performed through the classical Hill estimator, a statistic strongly dependent on the number k of top order statistics used, and with a high asymptotic bias as k increases, unless the underlying model is a strict Pareto model. First, on the basis of the asymptotic structure of Hill's estimator for different k-values, we propose "asymptotically best linear (BL) unbiased" estimators of the tail index. A similar derivation on the basis of the log-excesses and of the scaled log-spacings is performed and the adequate weights for the largest log-observations are provided. The asymptotic behaviour of those estimators is derived, and they are compared with other alternative estimators, both asymptotically and for finite samples. As an overall conclusion we may say that even asymptotic equivalent estimators may exhibit very diversified finite sample properties.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 25