A location invariant moment-type estimator II
Authors:
Cheng-Xiu Ling, Zuoxiang Peng and Saralees Nadarajah
Journal:
Theor. Probability and Math. Statist. 77 (2008), 177-189
MSC (2000):
Primary 60F99
DOI:
https://doi.org/10.1090/S0094-9000-09-00756-X
Published electronically:
January 21, 2009
MathSciNet review:
2432781
Full-text PDF Free Access
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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.
References
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References
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- Z. Fan, Estimation problems for distributions with heavy tails, J. Statist. Plann. Inference 123 (2004), 13–40. MR 2058119 (2005c:62059)
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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
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