Eigenstructures of spatial design matrices

David J. Gorsich, Marc Genton, Gilbert Strang

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In estimating the variogram of a spatial stochastic process, we use a spatial design matrix. This matrix is the key to Matheron’s variogram estimator. We show how the structure of the matrix for any dimension is based on the one-dimensional spatial design matrix, and we compute explicit eigenvalues and eigenvectors for all dimensions. This design matrix involves Kronecker products of second order finite difference matrices, with cosine eigenvectors and eigenvalues. Using the eigenvalues of the spatial design matrix, the statistics of Matheron’s variogram estimator are determined. Finally, a small simulation study is performed.

Original languageEnglish (US)
Pages (from-to)138-165
Number of pages28
JournalJournal of Multivariate Analysis
Volume80
Issue number1
DOIs
StatePublished - Jan 1 2002

Keywords

  • Discrete cosine transform
  • Eigenvalue
  • Eigenvector
  • Kriging
  • Kronecker product
  • Matheron’s estimator
  • Spatial statistics
  • Variogram

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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