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On the Use of the Variogram in Checking for Independence in Spatial Data
Author(s) -
Diblasi A.,
Bowman A. W.
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00211.x
Subject(s) - variogram , smoothing , statistics , nonparametric statistics , statistic , independence (probability theory) , mathematics , spatial analysis , test statistic , gaussian , spatial correlation , kriging , scale (ratio) , orthogonality , gaussian process , computer science , statistical hypothesis testing , cartography , geography , physics , geometry , quantum mechanics
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.