  Determining the relevant spatial covariates is one of the most important
problems in the analysis of point patterns. Parametric methods may lead to
incorrect conclusions, especially when the model of interactions between points
is wrong. Therefore, we propose a fully nonparametric approach to testing
significance of a covariate, taking into account the possible effects of
nuisance covariates. Our tests match the nominal significance level, and their
powers are comparable with the powers of parametric tests in cases where both
the model for intensity function and the model for interactions are correct.
When the parametric model for the intensity function is wrong, our tests
achieve higher powers. The proposed methods rely on Monte Carlo testing and
take advantage of the newly introduced covariate-weighted residual measure. We
also define a correlation coefficient between a point process and a covariate
and a partial correlation coefficient quantifying the dependence between a
point process and a covariate of interest while removing the influence of
nuisance covariates.
