Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction
Article first published online: 22 AUG 2006
Copyright © 2006 John Wiley & Sons, Ltd.
Special Issue: Special Issue on TIES Conference 2004
Volume 17, Issue 6, pages 635–652, September 2006
How to Cite
Zimmerman, D. L. (2006), Optimal network design for spatial prediction, covariance parameter estimation, and empirical prediction. Environmetrics, 17: 635–652. doi: 10.1002/env.769
- Issue published online: 22 AUG 2006
- Article first published online: 22 AUG 2006
- Manuscript Accepted: 14 JUL 2005
- Manuscript Received: 29 OCT 2004
- network design;
- optimal design;
- parameter estimation;
- spatial prediction
Inferences for spatial data are affected substantially by the spatial configuration of the network of sites where measurements are taken. In this article, criteria for network design that emphasize the utility of the network for prediction (kriging) of unobserved responses assuming known spatial covariance parameters are contrasted with criteria that emphasize the estimation of the covariance parameters themselves. It is shown, via a series of related examples, that these two main design objectives are largely antithetical and thus lead to quite different “optimal” designs. Furthermore, a hybrid design criterion that accounts for the effect that the sampling variation of spatial covariance parameter estimates has on prediction is described and illustrated. Situations in which the hybrid optimal design resembles designs that are optimal with respect to each of the other two criteria are identified. An application to the optimal augmentation of an acid deposition monitoring network in the eastern US is presented. Copyright © 2006 John Wiley & Sons, Ltd.