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On the Use of the Variogram in Checking for Independence in Spatial Data

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  • A. Diblasi
  • A. W. Bowman

Abstract

Summary. The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow‐up. An example is discussed.

Suggested Citation

  • A. Diblasi & A. W. Bowman, 2001. "On the Use of the Variogram in Checking for Independence in Spatial Data," Biometrics, The International Biometric Society, vol. 57(1), pages 211-218, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:211-218
    DOI: 10.1111/j.0006-341X.2001.00211.x
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    References listed on IDEAS

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    1. Diblasi, Angela & Bowman, Adrian, 1997. "Testing for constant variance in a linear model," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 95-103, April.
    2. Adrian Bowman & Stuart Young, 1996. "Graphical Comparison of Nonparametric Curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(1), pages 83-98, March.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "Rejoinder on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 442-447, September.
    2. Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
    3. Bowman, Adrian W. & Crujeiras, Rosa M., 2013. "Inference for variograms," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 19-31.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    5. Andrea Meilán-Vila & Jean D. Opsomer & Mario Francisco-Fernández & Rosa M. Crujeiras, 2020. "A goodness-of-fit test for regression models with spatially correlated errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 728-749, September.

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