A location invariant moment-type estimator II

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

doi:10.1090/S0094-9000-09-00756-X

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
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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.

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