Open Access
February 2017 Asymptotic properties of spatial scan statistics under the alternative hypothesis
Tonglin Zhang, Ge Lin
Bernoulli 23(1): 89-109 (February 2017). DOI: 10.3150/15-BEJ727


A common challenge for most spatial cluster detection methods is the lack of asymptotic properties to support their validity. As the spatial scan test is the most often used cluster detection method, we investigate two important properties in the method: the consistency and asymptotic local efficiency. We address the consistency by showing that the detected cluster converges to the true cluster in probability. We address the asymptotic local efficiency by showing that the spatial scan statistic asymptotically converges to the square of the maximum of a Gaussian random field, where the mean and covariance functions of the Gaussian random field depends on a function of at-risk population within and outside of the cluster. These conclusions, which are also supported by simulation and case studies, make it practical to precisely detect and characterize a spatial cluster.


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Tonglin Zhang. Ge Lin. "Asymptotic properties of spatial scan statistics under the alternative hypothesis." Bernoulli 23 (1) 89 - 109, February 2017.


Received: 1 July 2014; Revised: 1 March 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 06673472
MathSciNet: MR3556767
Digital Object Identifier: 10.3150/15-BEJ727

Keywords: asymptotic distribution , Clusters , converges in probability , Gaussian random field , spatial scan statistics

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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