Local asymptotic normality in a stationary model for spatial extremes

Michael Falk

Journal of Multivariate Analysis, 2011, vol. 102, issue 1, 48-60

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.

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 (search for similar items in EconPapers)
Date: 2011
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