Nonparametric spatial covariance functions

Estimation and testing

Ottar N. Bjornstad, Wilhelm Falck

Research output: Contribution to journalArticle

298 Citations (Scopus)

Abstract

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
Volume8
Issue number1
DOIs
StatePublished - Jan 1 2001

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Covariance Estimation
Function Estimation
Covariance Function
Envelope
Testing
Spline
Spatial Autocorrelation
Spatial Statistics
autocorrelation
confidence interval
Nonparametric Estimator
Positive semidefinite
Spatial Correlation
Correlation Length
Synthetic Data
Entire Function
Statistical Inference
grass
Bootstrap
Confidence

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Environmental Science(all)
  • Statistics, Probability and Uncertainty

Cite this

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Nonparametric spatial covariance functions : Estimation and testing. / Bjornstad, Ottar N.; Falck, Wilhelm.

In: Environmental and Ecological Statistics, Vol. 8, No. 1, 315918, 01.01.2001, p. 53-70.

Research output: Contribution to journalArticle

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