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Family of power divergence spatial scan statistics

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  • Zhang, Tonglin
  • Lin, Ge

Abstract

The classical spatial scan test, which derived by maximizing the likelihood ratio statistic over a collection of cluster candidates, is widely used in spatial cluster detection. As the likelihood ratio statistic is only a special case in the family of power divergence (PD) goodness-of-fit statistics, the classical spatial scan test is extended to the family of PD spatial scan tests. Therefore, the family of PD spatial scan tests includes not only the classical case but also many other cases. The test statistics, the asymptotic null distribution, and the methods to incorporate overdispersion in the cluster detection are derived. It is found that in the absence of independent variables, the asymptotic null distribution of the PD spatial scan statistics only depends on the ratio of at risks populations and the collection of cluster candidates. Particularly, the focus is on three special cases in the family. They are the deviance, the Pearson, and the Freeman–Tukey spatial scan tests, where the deviance spatial scan test is equivalent to the classical spatial scan test. In simulation studies, it is found that the three test statistics are almost equally powerful for cluster detection.

Suggested Citation

  • Zhang, Tonglin & Lin, Ge, 2014. "Family of power divergence spatial scan statistics," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 162-178.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:162-178
    DOI: 10.1016/j.csda.2014.02.003
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    References listed on IDEAS

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    1. Zhang, Tonglin & Lin, Ge, 2009. "Spatial scan statistics in loglinear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2851-2858, June.
    2. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
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    2. Kunihiko Takahashi & Hideyasu Shimadzu, 2018. "Multiple-cluster detection test for purely temporal disease clustering: Integration of scan statistics and generalized linear models," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-15, November.
    3. Goel, Varun & Kumar, Naresh & Singh, Paramvir, 2018. "Impact of modified parameters on diesel engine characteristics using biodiesel: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 82(P3), pages 2716-2729.

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