Local asymptotic normality in a stationary model for spatial extremes
De Haan and Pereira (2006) [6] provided models for spatial extremes in the case of stationarity, which depend on just one parameter [beta]>0 measuring tail dependence, and they proposed different estimators for this parameter. We supplement this framework by establishing local asymptotic normality (LAN) of a corresponding point process of exceedances above a high multivariate threshold. Standard arguments from LAN theory then provide the asymptotic minimum variance within the class of regular estimators of [beta]. It turns out that the relative frequency of exceedances is a regular estimator sequence with asymptotic minimum variance, if the underlying observations follow a multivariate extreme value distribution or a multivariate generalized Pareto distribution.
Year of publication: |
2011
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Authors: | Falk, Michael |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 102.2011, 1, p. 48-60
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Publisher: |
Elsevier |
Keywords: | Extreme value analysis Spatial extremes Multivariate exceedances Multivariate extreme value distribution Multivariate generalized Pareto distribution Local asymptotic normality LAN Regular estimator sequence Asymptotic efficiency |
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