  In this paper, we examine the validity of non-parametric spatial bootstrap as
a procedure to quantify errors in estimates of N-point correlation functions.
We do this by means of a small simulation study with simple point process
models and estimating the two-point correlation functions and their errors. The
coverage of confidence intervals obtained using bootstrap is compared with
those obtained from assuming Poisson errors. The bootstrap procedure considered
here is adapted for use with spatial (i.e. dependent) data. In particular, we
describe a marked point bootstrap where, instead of resampling points or blocks
of points, we resample marks assigned to the data points. These marks are
numerical values that are based on the statistic of interest. We describe how
the marks are defined for the two- and three-point correlation functions. By
resampling marks, the bootstrap samples retain more of the dependence structure
present in the data. Furthermore, this method of bootstrap can be performed
much quicker than some other bootstrap methods for spatial data, making it a
more practical method with large datasets. We find that with clustered point
datasets, confidence intervals obtained using the marked point bootstrap has
empirical coverage closer to the nominal level than the confidence intervals
obtained using Poisson errors. The bootstrap errors were also found to be
closer to the true errors for the clustered point datasets.
