Global envelope tests for spatial processes

• 成果类型: Article
• 署名作者: Myllymaki, Mari; Mrkvicka, Tomas; Grabarnik, Pavel; Seijo, Henri; Hahn, Ute
• 署名单位: Natural Resources Institute Finland (Luke); University of South Bohemia Ceske Budejovice; Russian Academy of Sciences; Pushchino Scientific Center for Biological Research (PSCBI) of the Russian Academy of Sciences; Institute of Physicohemical & Biological Problems of Soil Science; Aalto University; Aarhus University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12172
• 发表日期: 2017
• 页码: 381-404
• 关键词: statistical-analysis; Poisson processes; brownian-motion; point-processes; P-values; inference; simulation; particles; POWER

摘要

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 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 and they yield p-values. We illustrate these tests by using simulated and real point pattern data.