  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. Our method needs a central limit theorem for
\beta-mixing random fields which is proved by extending Bernstein's blocking
technique to non-cubic index sets and seems to be of interest in its own right.
By large-scale model-based simulations the performance of our test is studied
in dependence of the model parameters which determine the range of spatial
correlations.
