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Title: Global envelope tests, with emphasis on spatial point processes Authors:  Mari Myllymaki - Natural Resources Institute Finland (Luke) (Finland) [presenting]
Tomas Mrkvicka - University of South Bohemia (Czech Republic)
Pavel Grabarnik - Institute of Physico-Chemical and Biological Problems in Soil Science (Russia)
Ute Hahn - Aarhus University (Denmark)
Abstract: Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical function $T(r)$ with its simulated counterparts from the null model. However, the type I error probability $\alpha$ is conventionally controlled for a fixed distance $r$ only, whereas the functions are inspected on an interval of distances $I$. We propose global envelope tests on $I$. These tests allow the a priori selection of the global $\alpha$ and they yield p-values. We further propose the global rank envelope test as a solution to the multiple testing problem for Monte Carlo tests. Therefore the rank test can be used also, for example, for goodness-of-fit tests with several test functions and for groups of point patterns. Furthermore, a new functional ANOVA test, with a graphical interpretation of the result, is obtained as an extension of the rank test. The tests are developed for summary functions of spatial point processes in the first place, but they can in principle be applied to any functional data or curves. An R library GET is provided for performing the tests.