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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

A location invariant moment-type estimator II


Authors: Cheng-Xiu Ling, Zuoxiang Peng and Saralees Nadarajah
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 77 (2007).
Journal: Theor. Probability and Math. Statist. 77 (2008), 177-189
MSC (2000): Primary 60F99
Published electronically: January 21, 2009
MathSciNet review: 2432781
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Abstract | References | Similar Articles | Additional Information

Abstract: The moment estimator (Dekkers et al. (1989)) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves (2001)) is only suitable for estimating positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new estimator is based on the original moment-type estimator, but it is made location invariant by a random shift. Its asymptotic normality is derived, in a semiparametric setup.


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Additional Information

Cheng-Xiu Ling
Affiliation: Department of Mathematics, Southwest Normal University, Chongqing 400715, People’s Republic of China

Zuoxiang Peng
Affiliation: Department of Mathematics, Southwest Normal University, Chongqing 400715, People’s Republic of China
Email: pzx@swu.edu.cn

Saralees Nadarajah
Affiliation: Department of Statistics, University of Nebraska–Lincoln, Lincoln, Nebraska 68583
Email: snadaraj@unlserve.unl.edu

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00756-X
PII: S 0094-9000(09)00756-X
Keywords: Extreme value index, location invariant property, moment estimation, asymptotic normality, order statistics, regular varying functions
Received by editor(s): November 29, 2005
Published electronically: January 21, 2009
Article copyright: © Copyright 2009 American Mathematical Society