Assessing Spatial Isotropy

Michael Sherman, Yongtao Guan, James A. Calvin

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter proposes an objective test of the isotropy assumption that applies to a large class of spatial structures. In a spatial data analysis the analyst typically requires knowledge of the underlying correlation structure in order to effectively model data. A common assumption for this structure is one of isotropy, the direction independent correlation. While graphical techniques are useful to check for isotropy, they are often difficult to assess and cannot be interpreted objectively. Specifically, no explicit knowledge of marginal or joint distributions of the process is necessary, and the shape of the random field can be quite irregular. It is found that a test for isotropy may be obtained by comparing semivariograms at lags with the same length but in different directions. As the semivariograms are typically unknown, a test is formed based on estimators of the semivariograms. In the nonparametric spirit, the strength of dependence in the random field is quantified by a model-free mixing condition.

Original languageEnglish (US)
Title of host publicationRecent Advances and Trends in Nonparametric Statistics
PublisherElsevier Inc.
Pages467-475
Number of pages9
ISBN (Print)9780444513786
DOIs
StatePublished - Oct 2003
Externally publishedYes

Fingerprint

Isotropy
Semivariogram
Random Field
Mixing Conditions
Correlation Structure
Spatial Structure
Spatial Data
Marginal Distribution
Joint Distribution
Data Model
Irregular
Data analysis
Estimator
Unknown
Necessary
Knowledge
Model

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sherman, M., Guan, Y., & Calvin, J. A. (2003). Assessing Spatial Isotropy. In Recent Advances and Trends in Nonparametric Statistics (pp. 467-475). Elsevier Inc.. https://doi.org/10.1016/B978-044451378-6/50032-6

Assessing Spatial Isotropy. / Sherman, Michael; Guan, Yongtao; Calvin, James A.

Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., 2003. p. 467-475.

Research output: Chapter in Book/Report/Conference proceedingChapter

Sherman, M, Guan, Y & Calvin, JA 2003, Assessing Spatial Isotropy. in Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., pp. 467-475. https://doi.org/10.1016/B978-044451378-6/50032-6
Sherman M, Guan Y, Calvin JA. Assessing Spatial Isotropy. In Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc. 2003. p. 467-475 https://doi.org/10.1016/B978-044451378-6/50032-6
Sherman, Michael ; Guan, Yongtao ; Calvin, James A. / Assessing Spatial Isotropy. Recent Advances and Trends in Nonparametric Statistics. Elsevier Inc., 2003. pp. 467-475
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