On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

• 成果类型: Article
• 署名作者: Wang, Wenjia; Tuo, Rui; Wu, C. F. Jeff
• 署名单位: Texas A&M University System; Texas A&M University College Station; University System of Georgia; Georgia Institute of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1598868
• 发表日期: 2020
• 页码: 920-930
• 关键词: linear predictions; Asymptotic Optimality; random-field

摘要

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 Matern correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matern correlation functions. for this article are available online.