Electronic Journal of Statistics

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

Bruno Ebner, Norbert Henze, Michael A. Klatt, and Klaus Mecke

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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.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 2873-2904.

Received: October 2017
First available in Project Euclid: 18 September 2018

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Poisson point process geometric functionals nonparametric methods threshold procedure astroparticle physics

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Ebner, Bruno; Henze, Norbert; Klatt, Michael A.; Mecke, Klaus. Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images. Electron. J. Statist. 12 (2018), no. 2, 2873--2904. doi:10.1214/18-EJS1467. https://projecteuclid.org/euclid.ejs/1537257628

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