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

Published online by Cambridge University Press:  14 July 2016

Noel Cressie
Noel Cressie*
Affiliation:
The Flinders University of South Australia
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Abstract

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.

Keywords

CLUSTERINGINVARIANCEKUIPER'S STATISTICPOISSON NOISEPOWERRECTANGULAR SIGNALSCAN STATISTICSUPREMUM
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 272 - 283
Copyright
Copyright © Applied Probability Trust 1977 

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