Theory & Methods: Partition‐based Goodness‐of‐fit Tests on the Line and the Circle
Carol J. Feltz, Gerald A. Goldin · Australian & New Zealand Journal of Statistics · 2001
This paper proposes a way of constructing new, consistent generalizations of the Cramér–von Mises test on the line, and the Watson Un2 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.