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1 results

  • On some properties of the scan statistic on the circle and the line

  • Noel Cressie
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 2 / June 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 272-283
    Print publication:
    June 1977

  • The scan statistic is defined as the supremum of a particular continuous-time stochastic process, and is used as a test statistic for testing uniformity against a simple clustering type of alternative. Its distribution under the null hypothesis is investigated and weak convergence of the stochastic process to the appropriate Gaussian process is proved. An interesting link is forged between the circular scan statistic and Kuiper's statistic, which rids us of the trouble of estimating a nuisance parameter. Distributions under the alternative are then derived, and asymptotic power comparisons are made.