Assessing the significance of the correlation between the components of a bivariate Gaussian random field

Moreno Bevilacqua, Ronny Vallejos, Daira Velandia

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the association between autocorrelated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution of the maximum likelihood estimator of a specific parametric class of bivariate covariance models. Explicit expressions for the Fisher information matrix are given for a separable and a nonseparable version of the parametric class, leading to an asymptotic test. The empirical evidence supports our proposal, and as a result, in most of the cases, the new test performs better than the modified t test even when the bivariate covariance model is misspecified or the distribution of the bivariate random field is not Gaussian. Finally, to illustrate how the proposed test works in practice, we study a real dataset concerning the relationship between arsenic and lead from a contaminated area in Utah, USA.

Original languageEnglish
Pages (from-to)545-556
Number of pages12
JournalEnvironmetrics
Volume26
Issue number8
DOIs
StatePublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Cross-covariance estimation
  • Geostatistics
  • Hypothesis testing
  • Increasing domain
  • Power function

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