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Biometrika 2008 95(4):831-845; doi:10.1093/biomet/asn045
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© 2008 Biometrika Trust

Articles

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

Yongtao Guan

Division of Biostatistics, Yale University, New Haven, Connecticut 06520-8034, U.S.A. yongtao.guan{at}yale.edu

Received for publication 1 April 2007. Revision received 1 March 2008.
  Abstract

We introduce a formal testing procedure to assess the fit of an inhomogeneous spatial Poisson process model, based on a discrepancy measure function Formula that is constructed from residuals obtained from the fitted model. We derive the asymptotic distributional properties of Formula 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.

Key Words: Goodness-of-fit test • Inhomogeneous spatial Poisson process • Residual diagnostic


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