Monte Carlo testing in spatial statistics, with applications to spatial residuals

This paper reviews recent advances made in testing in spatial statistics and discussed at the Spatial Statistics conference in Avignon 2015. The rank and directional quantile envelope tests are discussed and practical rules for their use are provided. These tests are global envelope tests with an appropriate type I error probability. Two novel examples are given on their usage. First, in addition to the test based on a classical one-dimensional summary function, the goodness-of-fit of a point process model is evaluated by means of the test based on a higher dimensional functional statistic, namely a two-dimensional smoothed residual field. Second, a goodness-of-fit test of a geostatistical model is performed based on two-dimensional raw residuals.