• Bernoulli
  • Volume 23, Number 1 (2017), 89-109.

Asymptotic properties of spatial scan statistics under the alternative hypothesis

Tonglin Zhang and Ge Lin

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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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Bernoulli, Volume 23, Number 1 (2017), 89-109.

Received: July 2014
Revised: March 2015
First available in Project Euclid: 27 September 2016

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asymptotic distribution clusters converges in probability Gaussian random field spatial scan statistics


Zhang, Tonglin; Lin, Ge. Asymptotic properties of spatial scan statistics under the alternative hypothesis. Bernoulli 23 (2017), no. 1, 89--109. doi:10.3150/15-BEJ727.

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