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August, 1980 The Asymptotic Distribution of the Scan Statistic Under Uniformity
Noel Cressie
Ann. Probab. 8(4): 828-840 (August, 1980). DOI: 10.1214/aop/1176994669


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.


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Noel Cressie. "The Asymptotic Distribution of the Scan Statistic Under Uniformity." Ann. Probab. 8 (4) 828 - 840, August, 1980.


Published: August, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0438.60035
MathSciNet: MR577319
Digital Object Identifier: 10.1214/aop/1176994669

Primary: 60G35
Secondary: 62E20

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

Rights: Copyright © 1980 Institute of Mathematical Statistics


Vol.8 • No. 4 • August, 1980
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