Statistical Science

A Review of Nonparametric Hypothesis Tests of Isotropy Properties in Spatial Data

Zachary D. Weller and Jennifer A. Hoeting

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Abstract

An important aspect of modeling spatially referenced data is appropriately specifying the covariance function of the random field. A practitioner working with spatial data is presented a number of choices regarding the structure of the dependence between observations. One of these choices is to determine whether or not an isotropic covariance function is appropriate. Isotropy implies that spatial dependence does not depend on the direction of the spatial separation between sampling locations. Misspecification of isotropy properties (directional dependence) can lead to misleading inferences, for example, inaccurate predictions and parameter estimates. A researcher may use graphical diagnostics, such as directional sample variograms, to decide whether the assumption of isotropy is reasonable. These graphical techniques can be difficult to assess, open to subjective interpretations, and misleading. Hypothesis tests of the assumption of isotropy may be more desirable. To this end, a number of tests of directional dependence have been developed using both the spatial and spectral representations of random fields. We provide an overview of nonparametric methods available to test the hypotheses of isotropy and symmetry in spatial data. We discuss important considerations in choosing a test, provide recommendations for implementing a test, compare several of the methods via a simulation study, and propose a number of open research questions. Several of the reviewed methods can be implemented in R using our package spTest, available on CRAN.

Article information

Source
Statist. Sci., Volume 31, Number 3 (2016), 305-324.

Dates
First available in Project Euclid: 27 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.ss/1475001231

Digital Object Identifier
doi:10.1214/16-STS547

Mathematical Reviews number (MathSciNet)
MR3552737

Zentralblatt MATH identifier
06946228

Keywords
Isotropy symmetry nonparametric spatial covariance

Citation

Weller, Zachary D.; Hoeting, Jennifer A. A Review of Nonparametric Hypothesis Tests of Isotropy Properties in Spatial Data. Statist. Sci. 31 (2016), no. 3, 305--324. doi:10.1214/16-STS547. https://projecteuclid.org/euclid.ss/1475001231


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