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 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: ordering the empirical and simulated functions on the basis of their r-wise ranks among each other, and the construction of envelopes for a deviation test. These new tests allow the a priori choice of the global α and they yield p-values. We illustrate these tests by using simulated and real point pattern data.
| Original language | English |
|---|---|
| Journal | Journal of the Royal Statistical Society, Series B (Statistical Methodology) |
| Volume | 79 |
| Issue | 2 |
| Pages (from-to) | 381-404 |
| Number of pages | 27 |
| ISSN | 1369-7412 |
| DOIs | |
| Publication status | Published - 1 Mar 2017 |
Keywords
- Deviation test
- Functional depth
- Global envelope test
- Goodness-of-fit test
- Monte Carlo p-value
- Spatial point pattern