Testing the complete spatial randomness by Diggle's test without an arbitrary upper limit

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Journal of Statistical Computation and Simulation, ISSN: 0094-9655, Vol: 76, Issue: 7, Page: 585-591

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Ho, L. P.; Chiu, S. N.
Informa UK Limited; Taylor & Francis
Mathematics; Complete spatial randomness; Edge-correction; Intensity estimator; K -function; Spatial point pattern
article description
Diggle's test for complete spatial randomness of a given point pattern uses the discrepancy between the estimated and the theoretical form of a summary function as the test statistic. One commonly used discrepancy measure is the supremum of the pointwise differences over a suitably chosen range; the upper bound of the range is an arbitrary but sometimes crucial parameter. This paper shows that when we use Ripley's K -function as the summary function, it is possible to avoid using an arbitrary upper bound by using adapted distance dependent intensity estimators.