Partition-based goodness-of-fit tests on the line and the circle

Carol J. Feltz, Gerald A. Goldin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This paper proposes a way of constructing new, consistent generalizations of the Cramérvon Mises test on the line, and the Watson U2n test on the circle, based on classes of partitions invariant under various groups of coordinate transformations. It is illustrated with a set of data where there is reason to look for clustering in more than one local region. The framework developed extends the authors' earlier work generalizing the Kolmogorov-Smirnov and Kuiper goodness-of-fit tests, and provides a conceptually unifying description. For this construction, the distribution for the null hypothesis does not have to be uniform, and tests can be invariant under general coordinate transformations. The properties of some specific tests are explored through numerical simulations.

Original languageEnglish (US)
Pages (from-to)207-220
Number of pages14
JournalAustralian and New Zealand Journal of Statistics
Issue number2
StatePublished - Jun 2001

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Cramér-von Mises test
  • Distribution-free tests
  • Kolmogorov-Smirnov test
  • Kuiper's test
  • Watson U test


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