On Prediction Properties of Kriging: Uniform Error Bounds and Robustness. Issue 530 (2nd April 2020)

• Record Type: Journal Article
• Authors: Wang, Wenjia; Tuo, Rui; Jeff Wu, C. F.
• Is Part Of: Journal of the American Statistical Association. Volume 115:Issue 530(2020)
• Page Start: 920
• Page End: 930
• Publication Date: 2020-04-02
• Subjects: Gaussian process modeling -- Radial basis functions -- Space-filling designs -- Spatial statistics -- Uniform convergence; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2019.1598868
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract: Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work, we obtain some error bounds for the simple and universal kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions. Supplementary materials for this article are available online.