Robust Prediction for Contaminated Random Field

• Activity Number: 398
• Type: Topic Contributed
• Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Baptiste Fournier*+
• Companies: Swiss Federal Institute of Technology
• Keywords: spatial statistics ; substitutive outliers ; robustness ; prediction

Abstract

The prediction problem in the presence of outliers is a general problem in spatial statistics. Methods to robustify the ordinary kriging exist, but they usually treat the case of additive outliers. Here, we deal with substitutive outliers. With a certain probability, each site independently exhibits an outlier with the expectation of the nominal process, but with larger variance. We derive the conditional expectation of the true process given the observed one. This turns out to be a sum of predictors, one for each scenario of outliers locations. The number of scenari is equal to two to the number of sites in the field. This is hopelessly complex for a grid of reasonable size. Therefore, the space of contamination scenari will be restricted. The way to proceed consists in two steps. First, detect the contaminated locations. Second, consider a neighborhood of the scenario found in the first step. The more we increase the size of the neighborhood, the better is the quality of the estimation with the drawback that the computational cost increases. We will present the theoretical background of the described method and also show some simulation results illustrating its performance.