Environmental and Ecological Statistics

, Volume 8, Issue 1, pp 53–70

Nonparametric spatial covariance functions: Estimation and testing

  • Ottar N. BjØrnstad
  • Wilhelm Falck

DOI: 10.1023/A:1009601932481

Cite this article as:
BjØrnstad, O.N. & Falck, W. Environmental and Ecological Statistics (2001) 8: 53. doi:10.1023/A:1009601932481


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 (Poa alpina).

bootstrapping dependent data correlogram geostatistis nonparametric regression population genetics smoothing spline spatial autocorrelation 

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Ottar N. BjØrnstad
    • 1
  • Wilhelm Falck
    • 3
  1. 1.NCEASSanta Barbara
  2. 2.Department of EntomologyPenn State UniversityUniversity Park
  3. 3.Department of Biology, Division of ZoologyUniversity of OsloBlindernNorway

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