| Spatial Dependence Estimation and Prediction for Max-stable Random Fields
| Daniel Cooley
University of Colorado-Boulder; Post-Doctorate, Colorado State University
Wednesday, January 31, 2007
IIn meteorological or environmental studies, data are recorded at specific
locations. With spatial data two immediate questions arise: how can
the spatial dependence be measured, and how can spatial prediction be
performed? If the data represents central tendencies of the process,
the field of geostatistics answers these questions using the variogram
and kriging. However, if the data are extreme observations, these
questions are largely unanswered.
To measure pairwise spatial dependence in max-stable random fields, we
propose the madogram. The madogram is simply a first-order variogram and
therefore has its roots in traditional geostatistics. However, the
madogram also has a convenient relationship with multivariate extreme-
value distributions and the extremal coefficient, an existing measure
of dependence for extremes. The madogram can be extended to provide an
estimate of the complete bivariate dependence structure, and proposed
madogram estimators are presented and compared to existing estimators.
To perform spatial prediction, we propose estimating the conditional
distribution of an unmonitored location given the observed values at nearby
locations. To estimate the conditional distribution, we utilize the spectral
measure of the max-stable distribution. Our ongoing work is to find an
appropriate parametric model for the spectral measure.