Spatially varying cross-correlation coefficients in the presence of nugget effects

William Kleiber, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between multiple processes. The key is to identify the cross-correlation coefficient matrix with a contraction matrix, which can be either diagonal, implying a parsimonious formulation, or a fully general contraction matrix, yielding greater flexibility but added model complexity. We illustrate the approach with a bivariate minimum and maximum temperature dataset in Colorado, allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations, while still yielding a positive definite covariance matrix. © 2012 Biometrika Trust.
Original languageEnglish (US)
Pages (from-to)213-220
Number of pages8
Issue number1
StatePublished - Nov 29 2012

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)


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