A location invariant moment-type estimator. I

Ling, Cheng-Xiu; Peng, Zuoxiang; Nadarajah, Saralees

doi:10.1090/S0094-9000-08-00728-X

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
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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.

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