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A goodness-of-fit test for inhomogeneous spatial Poisson processes

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  • Yongtao Guan

Abstract

We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of and develop a test statistic based on them. Our test statistic has a limiting standard normal distribution, so that the test can be performed by simply comparing the test statistic with readily available critical values. We perform a simulation study to assess the performance of the proposed method and apply it to a real data example. Copyright 2008, Oxford University Press.

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  • Yongtao Guan, 2008. "A goodness-of-fit test for inhomogeneous spatial Poisson processes," Biometrika, Biometrika Trust, vol. 95(4), pages 831-845.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:831-845
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    File URL: http://hdl.handle.net/10.1093/biomet/asn045
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    Cited by:

    1. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    2. Baddeley, Adrian & Hardegen, Andrew & Lawrence, Thomas & Milne, Robin K. & Nair, Gopalan & Rakshit, Suman, 2017. "On two-stage Monte Carlo tests of composite hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 75-87.

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