Spatial Dependence Estimation and Prediction for Max-stable Random Fields
Daniel Cooley

Ph.D., University of Colorado-Boulder; Post-Doctorate, Colorado State University

Wednesday, January 31, 2007
3:10 p.m.
D104 Engineering

In 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.





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