The extent of the maximum likelihood estimator for the extreme value index
In extreme value analysis, staring from Smith (1987) [1], the maximum likelihood procedure is applied in estimating the shape parameter of tails--the extreme value index [gamma]. For its theoretical properties, Zhou (2009) [12] proved that the maximum likelihood estimator eventually exists and is consistent for [gamma]>-1 under the first order condition. The combination of Zhou (2009) [12] and Drees et al (2004) [11] provides the asymptotic normality under the second order condition for [gamma]>-1/2. This paper proves the asymptotic normality for -1<[gamma]<=-1/2 and the non-consistency for [gamma]<-1. These results close the discussion on the theoretical properties of the maximum likelihood estimator.
Year of publication: |
2010
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Authors: | Zhou, Chen |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 101.2010, 4, p. 971-983
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Publisher: |
Elsevier |
Keywords: | Maximum likelihood Extreme value index Asymptotic normality |
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