Covariance tapering for interpolation of large spatial datasets

Reinhard Furrer*, Marc Genton, Douglas Nychka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

338 Scopus citations

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 languageEnglish (US)
Pages (from-to)502-523
Number of pages22
JournalJournal of Computational and Graphical Statistics
Volume15
Issue number3
DOIs
StatePublished - Sep 1 2006

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

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