We develop new tools for formal inference and informal model validation in
the analysis of spatial point pattern data. The score test is generalized to a
"pseudo-score" test derived from Besag's pseudo-likelihood, and to a class of
diagnostics based on point process residuals. The results lend theoretical
support to the established practice of using functional summary statistics,
such as Ripley's K-function, when testing for complete spatial randomness;
and they provide new tools such as the compensator of the K-function for
testing other fitted models. The results also support localization methods such
as the scan statistic and smoothed residual plots. Software for computing the
diagnostics is provided.Comment: Published in at http://dx.doi.org/10.1214/11-STS367 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
