Abstract
Interpolation of a spatially correlated random process is used in many scientific areas. The best unbiased linear predictor, often called a kriging predictor in geostatistical science, requires the solution of a (possibly large) linear system based on the covariance matrix of the observations. In this article, we show that tapering the correct covariance matrix with an appropriate compactly supported positive definite function reduces the computational burden significantly and still leads to an asymptotically optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. Monte Carlo simulations support the theoretical results. An application to a large climatological precipitation dataset is presented as a concrete and practical illustration.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 502-523 |
| Number of pages | 22 |
| Journal | JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2006 |
| Externally published | Yes |
Bibliographical note
Funding Information:The research of Furrer and Nychka was supported in part by the Geophysical Statistics Project at the National Center for Atmospheric Research under the NSF grants DMS-9815344 and DMS-0355474. The work of Genton was partially supported by NSF grant DMS-0504896
Keywords
- Asymptotic optimality
- Compactly supported covariance
- Kriging
- Large linear systems
- Sparse matrix
ASJC Scopus subject areas
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Statistics, Probability and Uncertainty