A semi-parameter estimator of a “scale” second order parameter based upon the log-excesses

Author

Gomes, M. Ivette ; Rodrigues, Lígia Henriques ; Pereira, Hugo ; Pestana, Dinis

Author_Institution

Fac. de Cienc., Univ. de Lisboa, Lisbon

fYear

2008

fDate

23-26 June 2008

Firstpage

329

Lastpage

334

Abstract

In this paper we are interested in the derivation of the asymptotic and finite-sample distributional properties of a ldquoquasi-maximum likelihoodrdquo estimator of a ldquoscalerdquo second order parameter beta, directly based on the log-excesses of an available sample. Such estimation is of primordial importance for the adaptive selection of the optimal sample fraction to be used in the classical semi-parametric tail index estimation as well as for the reduced-bias estimation of the tail index, high quantiles and other parameters of extreme or even rare events.

Keywords

maximum likelihood estimation; sampling methods; statistical distributions; asymptotic distributional properties; finite-sample distributional properties; log-excesses; quasimaximum likelihood estimator; reduced-bias estimation; scale second order parameter; semiparametric tail index estimation; Biological system modeling; Delta modulation; Distribution functions; Insurance; Maximum likelihood estimation; Pareto analysis; Probability distribution; Statistical distributions; Statistics; Tail; Statistics of extremes; heavy tails; log-excesses; maximum-likelihood; semi-parametric estimation; simulation;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Technology Interfaces, 2008. ITI 2008. 30th International Conference on

Conference_Location

Dubrovnik

ISSN

1330-1012

Print_ISBN

978-953-7138-12-7

Electronic_ISBN

1330-1012

Type

conf

DOI

10.1109/ITI.2008.4588431

Filename

4588431