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Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images

Ebner, Bruno 1; Henze, Norbert 1; Klatt, Michael A. 1; Mecke, K.
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)


We propose a class of goodness-of-fit tests for complete spatial randomness (CSR). In contrast to standard tests, our procedure utilizes a transformation of the data to a binary image, which is then characterized by geometric functionals. Under a suitable limiting regime, we derive the asymptotic distribution of the test statistics under the null hypothesis and almost sure limits under certain alternatives. The new tests are computationally efficient, and simulations show that they are strong competitors to other tests of CSR. The tests are applied to a real data set in gamma-ray astronomy, and immediate extensions are presented to encourage further work.

Verlagsausgabe §
DOI: 10.5445/IR/1000086246
Veröffentlicht am 05.10.2018
DOI: 10.1214/18-EJS1467
Zitationen: 10
Zitationen: 10
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 1935-7524
KITopen-ID: 1000086246
Erschienen in Electronic journal of statistics
Verlag Institute of Mathematical Statistics (IMS)
Band 12
Heft 2
Seiten 2873-2904
Schlagwörter Poisson point process, geometric functionals, nonparametric methods, threshold procedure, astroparticle physics
Nachgewiesen in Dimensions
Web of Science
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