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Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function

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  • Davies, Tilman M.
  • Jones, Khair
  • Hazelton, Martin L.

Abstract

The spatial relative risk function is now regarded as a standard tool for visualising spatially tagged case-control data. This function is usually estimated using the ratio of kernel density estimates. In many applications, spatially adaptive bandwidths are essential to handle the extensive inhomogeneity in the distribution of the data. Earlier methods have employed separate, asymmetrical smoothing regimens for case and control density estimates. However, we show that this can lead to potentially misleading methodological artefacts in the resulting estimates of the log-relative risk function. We develop a symmetric adaptive smoothing scheme that addresses this problem. We study the asymptotic properties of the new log-relative risk estimator, and examine its finite sample performance through an extensive simulation study based on a number of problems adapted from real life applications. The results are encouraging.

Suggested Citation

  • Davies, Tilman M. & Jones, Khair & Hazelton, Martin L., 2016. "Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 12-28.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:12-28
    DOI: 10.1016/j.csda.2016.02.008
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    References listed on IDEAS

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    1. Clark, Allan B. & Lawson, Andrew B., 2004. "An evaluation of non-parametric relative risk estimators for disease maps," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 63-78, August.
    2. Marshall, Jonathan C. & Hazelton, Martin L., 2010. "Boundary kernels for adaptive density estimators on regions with irregular boundaries," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 949-963, April.
    3. Davies, Tilman M. & Hazelton, Martin L. & Marshall, Jonathan. C, 2011. "sparr: Analyzing Spatial Relative Risk Using Fixed and Adaptive Kernel Density Estimation in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i01).
    4. Peter J. Diggle, 1990. "A Point Process Modelling Approach to Raised Incidence of a Rare Phenomenon in the Vicinity of a Prespecified Point," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 153(3), pages 349-362, May.
    5. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
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    Cited by:

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    3. Davies, Tilman M. & Flynn, Claire R. & Hazelton, Martin L., 2018. "On the utility of asymptotic bandwidth selectors for spatially adaptive kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 75-81.
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    5. Michael Govorov & Giedrė Beconytė & Gennady Gienko, 2023. "Trivariate Kernel Density Estimation of Spatiotemporal Crime Events with Case Study for Lithuania," Sustainability, MDPI, vol. 15(11), pages 1-17, May.

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