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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

Abstract

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. https://doi.org/10.1214/aop/1176994669

Information

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

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

Subjects:
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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