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April 2000 Tail probabilities for the null distribution of scanning statistics
David Siegmund, Benjamin Yakir
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Bernoulli 6(2): 191-213 (April 2000).


This paper is concerned with statistics that scan a multidimensional spatial region to detect a signal against a noisy background. The background is modelled as independent observations from an exponential family of distributions with a known `null' value of the natural parameter, while the signal is given by independent observations from the same exponential family, but with a different value of the parameter on a particular subregion of the spatial domain. The main result is an extension to multidimensional time of the method of Pollak and Yakir, which relies on a change of measure motivated by change-point analysis, to evaluate approximately the null distribution of the likelihood ratio statistic. Both large-deviation and Poisson approximations are obtained.


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David Siegmund. Benjamin Yakir. "Tail probabilities for the null distribution of scanning statistics." Bernoulli 6 (2) 191 - 213, April 2000.


Published: April 2000
First available in Project Euclid: 12 April 2004

zbMATH: 0976.62048
MathSciNet: MR2001E:62036

Keywords: Change-point , likelihood ratio , scan statistic

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability

Vol.6 • No. 2 • April 2000
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