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A Bivariate Cramér–Von Mises Type of Test for Spatial Randomness

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  • Dale L. Zimmerman

Abstract

A test for the randomness of a mapped spatial pattern of events in a rectangle D in R2 is examined that is based on the ‘distance’ between the bivariate empirical distribution function of the events' Cartesian co‐ordinates and the uniform distribution function. The distance between distribution functions is measured by a modification of the bivariate Cramér–von Mises statistic that is invariant to the corner of D identified as the origin. This invariance property, which is essential, is lacking in the standard bivariate Cramér–von Mises statistic. Several real examples and results from simulation indicate that the test proposed is superior to existing tests for detecting heterogeneous alternatives to spatial randomness but inferior for detecting regular or aggregated alternatives. Some additional features of the test are its computational simplicity, the non‐necessity of adjusting for edge effects and the ease with which it can be extended to test for certain types of heterogeneity.

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  • Dale L. Zimmerman, 1993. "A Bivariate Cramér–Von Mises Type of Test for Spatial Randomness," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(1), pages 43-54, March.
    • Handle: RePEc:bla:jorssc:v:42:y:1993:i:1:p:43-54
    DOI: 10.2307/2347408
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    Cited by:

    1. Frederic Paik Schoenberg, 2004. "Testing Separability in Spatial-Temporal Marked Point Processes," Biometrics, The International Biometric Society, vol. 60(2), pages 471-481, June.
    2. Petrie, Adam & Willemain, Thomas R., 2013. "An empirical study of tests for uniformity in multidimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 253-268.
    3. Petrie, Adam, 2016. "Graph-theoretic multisample tests of equality in distribution for high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 145-158.
    4. Heinrich Lothar & Klein Stella, 2011. "Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 359-387, December.

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