Bootstrapping a Spatial

We consider the problem of resampling or bootstrapping a point process to get con dence intervals for the reduced second moment function We propose a resampling scheme for spatial data which we call the marked point method This is a variant of the block of blocks bootstrap rst introduced by K unsch A simulation study with a Poisson a clustered and a regular point process on the unit square in R shows that the marked point method yields con dence intervals that are closer to the nominal level than resampling by tiling block bootstrap and by using subsets subsampling The con dence intervals obtained by the marked point method also tend to be shorter after accounting for di erences in empirical coverage Finally the marked point method is very much computationally less intensive so that even with moderate sample sizes the marked point method takes considerably less computing time We also nd that the simple method of dividing the sample and treating the subsamples as independent replicates works reasonably well We apply some of these methods to a set of astronomy data