A location invariant moment-type estimator. I
Authors:
Cheng-Xiu Ling, Zuoxiang Peng and Saralees Nadarajah
Journal:
Theor. Probability and Math. Statist. 76 (2008), 23-31
MSC (2000):
Primary 60F99
DOI:
https://doi.org/10.1090/S0094-9000-08-00728-X
Published electronically:
July 10, 2008
MathSciNet review:
2368736
Full-text PDF Free Access
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Additional Information
Abstract: The moment’s 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 to estimate 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 is made location invariant by a random shift. Its weak consistency and strong consistency are derived, in a semiparametric setup.
References
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References
- S. Cheng and L. de Haan, Penultimate approximation for Hill’s estimator, Scand. J. Statist. 28 (2001), 569–575. MR 1858418 (2002h:62156)
- S. Cheng and J. Pan, Asymptotic expansions of estimators for the tail index with applications, Scand. J. Statist. 25 (1998), 717–728. MR 1666796 (2000d:62079)
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- L. de Haan and U. Stadtmüller, Generalized regular variation of second order, J. Aust. Math. Soc., A 61 (1996), 381–395. MR 1420345 (97g:26001)
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- B. M. Hill, A simple general approach to inference about the tail of a distribution, Ann. Statist. 3 (1975), 1163–1174. MR 0378204 (51:14373)
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Additional Information
Cheng-Xiu Ling
Affiliation:
Department of Mathematics, Southwest Normal University, Chongqing 400715, P. R. China
Email:
pzx@swu.edu.cn
Zuoxiang Peng
Affiliation:
Department of Mathematics, Southwest Normal University, Chongqing 400715, P. R. China
Saralees Nadarajah
Affiliation:
Department of Statistics, University of Nebraska–Lincoln, Lincoln, Nebraska 68583, USA
Email:
snadaraj@unlserve.unl.edu
Keywords:
Extreme value index,
location invariant property,
moment estimation,
strong and weak consistencies,
order statistics,
regular varying functions
Received by editor(s):
November 29, 2005
Published electronically:
July 10, 2008
Article copyright:
© Copyright 2008
American Mathematical Society