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Biometrika 2009 96(1):1-17; doi:10.1093/biomet/asp001
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© 2009 Biometrika Trust

Articles

Modelling pairwise dependence of maxima in space

Philippe Naveau

Laboratoire des Sciences du Climat et de l'Environnement, LSCE-IPSL-CNRS, 91191 Gif-sur-Yvette, France naveau{at}lsce.ipsl.fr

Armelle Guillou

Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg Cedex, France guillou{at}math.u-strasbg.fr

Daniel Cooley

Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, U.S.A. cooleyd{at}stat.colostate.edu

Jean Diebolt

Laboratoire Analyse et Mathématiques Appliquées, CNRS, Université de Marne-la Vallée, 77454 Marne-la Vallée, France e.diebolt{at}noos.fr

Received for publication 1 May 2006. Revision received 1 August 2008.
  Abstract

We model pairwise dependence of temporal maxima, such as annual maxima of precipitation, that have been recorded in space, either on a regular grid or at irregularly spaced locations. The construction of our estimators stems from the variogram concept. The asymptotic properties of our pairwise dependence estimators are established through properties of empirical processes. The performance of our approach is illustrated by simulations and by the treatment of a real dataset. In addition to bringing new results about the asymptotic behaviour of copula estimators, the latter being linked to first-order variograms, one main advantage of our approach is to propose a simple connection between extreme value theory and geostatistics.

Key Words: Copula • Extreme value theory • Spatial statistic • Variogram


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