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We consider spatially homogeneous marked point patterns in an unboundedlyexpanding convex sampling window. Our main objective is to identify thedistribution of the typical mark by constructing an asymptotic$\chi^2$-goodness-of-fit test. The corresponding test statistic is based on anatural empirical version of the Palm mark distribution and a smoothedcovariance estimator which turns out to be mean square consistent. Our approachdoes not require independent marks and allows dependences between the markfield and the point pattern. Instead we impose a suitable $\beta$-mixingcondition on the underlying stationary marked point process which can bechecked for a number of Poisson-based models and, in particular, in the case ofgeostatistical marking. In order to study test performance, our test approachis applied to detect anisotropy of specific Boolean models.

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