Global Envelope Tests for Spatial Processes

Research output: Research - peer-reviewJournal article


  • Mari Myllymäki
    Mari MyllymäkiFinland
  • Tomáš Mrkvička
    Tomáš MrkvičkaCzech Republic
  • Pavel Grabarnik
    Pavel GrabarnikRussian Federation
  • Henri Seijo
    Henri SeijoFinland
  • Ute Hahn
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 α is conventionally controlled for a fixed distance r only, whereas the functions are inspected on an interval of distances I. In this study, we propose two approaches related to Barnard’s Monte Carlo test for building global envelope tests on I: (1) ordering the empirical and simulated functions based on their r-wise ranks among each other, and (2) the construction of envelopes for a deviation test. These new tests allow the a priori selection of the global α and they yield p-values. We illustrate these tests using simulated and real point pattern data.
Original languageEnglish
JournalRoyal Statistical Society. Journal. Series B: Statistical Methodology
Issue number2
Pages (from-to)381-404
Number of pages27
StatePublished - 20 Mar 2017

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