Title

Asymptotic properties of spatial scan statistics under the alternative hypotheses

Editors

Ge L Kan (Ed.)

Document Type

Article

Publication Date

2-1-2017

Publication Title

Bernoulli

Volume

23

Issue

1

First page number:

89

Last page number:

109

Abstract

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.

Keywords

Asymptotic distribution, Clusters, Converges in probability, Gaussian random field, Spatial scan statistics

Language

eng

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