• Bernoulli
  • Volume 20, Number 4 (2014), 1673-1697.

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

Lothar Heinrich, Sebastian Lück, and Volker Schmidt

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We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^{2}$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.

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Bernoulli, Volume 20, Number 4 (2014), 1673-1697.

First available in Project Euclid: 19 September 2014

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$\beta$-mixing point process empirical Palm mark distribution reduced factorial moment measures smoothed covariance estimation $\chi^{2}$-goodness-of-fit test


Heinrich, Lothar; Lück, Sebastian; Schmidt, Volker. Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks. Bernoulli 20 (2014), no. 4, 1673--1697. doi:10.3150/13-BEJ523.

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