Nonparametric spatial covariance functions: Estimation and testing

Ottar N. Bjørnstad, Wilhelm Falck

Research output: Contribution to journalArticlepeer-review

420 Scopus citations


Spatial autocorrelation techniques are commonly used to describe genetic and ecological patterns. To improve statistical inference about spatial covariance, we propose a continuous nonparametric estimator of the covariance function in place of the spatial correlogram. The spline correlogram is an adaptation of a recent development in spatial statistics and is a generalization of the commonly used correlogram. We propose a bootstrap algorithm to erect a confidence envelope around the entire covariance function. The meaning of this envelope is discussed. Not all functions that can be drawn inside the envelope are candidate covariance functions, as they may not be positive semidefinite. However, covariance functions that do not fit, are not supported by the data. A direct estimate of the L0 spatial correlation length with associated confidence interval is offered and its interpretation is discussed. The spline correlogram is found to have high precision when applied to synthetic data. For illustration, the method is applied to electrophoretic data of an alpine grass (Pou alpina).

Original languageEnglish (US)
Article number315918
Pages (from-to)53-70
Number of pages18
JournalEnvironmental and Ecological Statistics
Issue number1
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Environmental Science
  • Statistics, Probability and Uncertainty


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