The Annals of Probability

The Asymptotic Distribution of the Scan Statistic Under Uniformity

Noel Cressie

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The problem of testing uniformity on [0, 1] against a clustering alternative, is considered. Naus has shown that the generalized likelihood ratio test yields the scan statistic $N(d)$. The asymptotic distribution of $N(d)$ under the null hypothesis of uniformity is considered herein, and related to the version of the scan statistic defined for points from a Poisson process. An application of the above yields distributional results for the supremum of a stationary Gaussian process with a correlation function that is tent-like in shape, until it flattens out at a constant negative value.

Article information

Ann. Probab., Volume 8, Number 4 (1980), 828-840.

First available in Project Euclid: 19 April 2007

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Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 62E20: Asymptotic distribution theory

A particular Gaussian process asymptotic distribution clustering alternative distribution Poisson process scan statistic supremum distribution uniform distribution


Cressie, Noel. The Asymptotic Distribution of the Scan Statistic Under Uniformity. Ann. Probab. 8 (1980), no. 4, 828--840. doi:10.1214/aop/1176994669.

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