Point and Block Prediction in Log-GaussianRandom Fields: The Non-Constant Mean Case Changxiang Rui Department of Mathematical Sciences University of Arkansas Abstract
This work considers the problems of optimal
point and block prediction in Log-Gaussian random fields with
non-constant mean functions depending linearly on unknown parameters
and arbi-trary known covariance functions. First, we generalize the
optimal point predictor obtained in De Oliveira (2006), who considered
the case of Log-Gaussian random fields with constant mean function, and
compare this predictor to the commonly used lognormal kriging point
predictor. Second, we show that previous results on optimal block
prediction cannot be extended to the case of random fields with
non-constant mean functions. Specifically, we show that both families
of predictors considered by De Oliveira lack an optimal predictor (in
mean square error sense).
Finally, we numerically compare two block predictors and show that one of them is uniformly better than the other. This is joint work with Victor De Oliveira, University of Texas, San Antonio |