A margin-free clustering algorithm appropriate for dependent maxima in the domain of attraction of an extreme-value copula
Eric Cormier · Oct 10, 2014
Date: 2014-10-10
Time: 15:30-16:30
Location: BURN 1205
Abstract:
Extracting relevant information in complex spatial-temporal data sets is of paramount importance in statistical climatology. This is especially true when identifying spatial dependencies between quantitative extremes like heavy rainfall. The paper of Bernard et al. (2013) develops a fast and simple clustering algorithm for finding spatial patterns appropriate for extremes. They develop their algorithm by adapting multivariate extreme-value theory to the context of spatial clustering. This is done by relating the variogram, a well-known distance used in geostatistics, to the extremal coefficient of a pair of joint maxima. This gives rise to a straightforward nonparametric estimator of this distance using the empirical distribution function. Their clustering approach is used to analyze weekly maxima of hourly precipitation recorded in France and a spatial pattern consistent with existing weather models arises. This applied talk is devoted to the validation and extension of this clustering approach. A simulation study using the multivariate logistic distribution as well as max-stable random fields shows that this approach provides accurate clustering when the maxima belong to an extreme-value distribution. Furthermore this clustering distance can be viewed as an average absolute rank difference, implying that it is appropriate for margin-free clustering of dependent variables. In particular it is appropriate for dependent maxima in the domain of attraction of an extreme-value copula.