Local asymptotic normality in a stationary model for spatial extremes
Abstract
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.Download Info
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Article provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 102 (2011)
Issue (Month): 1 (January)
Pages: 48-60
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Related research
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;References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
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