Geostatistics

  • Robust Variograms The variogram of a stationary spatial process Y(s) is defined as E((Y(u)-Y(v))^2) and depends only on the distance |u-v|. The classical estimator of this quantity is the method of moment estimator. We have studied robust alternatives based on high-breakdown scale estimators and have studied their statistical properties. Based on estimates of the variogram at a few values of |u-v|, one can fit parametric functions. This idea has also been explored.

  • Principal Components for Multivariate Measurements Principal components are linear combinations of variables having maximal variance. Generalizing this technique to projection indices other than the variance has been a topic of interest in our group. We have made a systematic study of such projection indices, in particular for clustering and have developed algorithms for optimizing complex indices.

  • State-Space Models for Geostatistics Geostatistical models are used to describe the spatial dependence of some variable. Such models can be based on hidden variables, which are not directly observable and which model some underlying physical process. Such state-space models have been developed in our group and applications to environmental pollution processes have been studied. /LI>